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Erpenbeck A, Gull E, Cohen G. Quantum Monte Carlo Method in the Steady State. PHYSICAL REVIEW LETTERS 2023; 130:186301. [PMID: 37204908 DOI: 10.1103/physrevlett.130.186301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2022] [Revised: 12/07/2022] [Accepted: 04/07/2023] [Indexed: 05/21/2023]
Abstract
We present a numerically exact steady-state inchworm Monte Carlo method for nonequilibrium quantum impurity models. Rather than propagating an initial state to long times, the method is directly formulated in the steady state. This eliminates any need to traverse the transient dynamics and grants access to a much larger range of parameter regimes at vastly reduced computational costs. We benchmark the method on equilibrium Green's functions of quantum dots in the noninteracting limit and in the unitary limit of the Kondo regime. We then consider correlated materials described with dynamical mean field theory and driven away from equilibrium by a bias voltage. We show that the response of a correlated material to a bias voltage differs qualitatively from the splitting of the Kondo resonance observed in bias-driven quantum dots.
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Affiliation(s)
- A Erpenbeck
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - E Gull
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - G Cohen
- The Raymond and Beverley Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel
- School of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel
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2
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Tong K, Dou W. Numerical study of non-adiabatic quantum thermodynamics of the driven resonant level model: non-equilibrium entropy production and higher order corrections. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:495703. [PMID: 36223783 DOI: 10.1088/1361-648x/ac99c8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2022] [Accepted: 10/12/2022] [Indexed: 06/16/2023]
Abstract
We present our numerical study on quantum thermodynamics of the resonant level model subjected to non-equilibrium condition as well as external driving. Following our previous work on non-equilibrium quantum thermodynamics (Douet al2020Phys. Rev.B101184304), we expand the density operator into a series of power in the driving speed, where we can determine the non-adiabatic thermodynamic quantities. Particularly, we calculate the non-equilibrium entropy production rate as well as higher order non-adiabatic corrections to the energy and/or population, which is not determined previously in Douet al(2020Phys. Rev.B101184304). In the limit of weak system-bath coupling, our results reduce to the one from the quantum master equation.
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Affiliation(s)
- Kaiyi Tong
- School of Science, Westlake University, Hangzhou, Zhejiang 310024, People's Republic of China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, People's Republic of China
| | - Wenjie Dou
- School of Science, Westlake University, Hangzhou, Zhejiang 310024, People's Republic of China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, People's Republic of China
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3
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Cohen G, Galperin M. Green’s function methods for single molecule junctions. J Chem Phys 2020; 152:090901. [DOI: 10.1063/1.5145210] [Citation(s) in RCA: 25] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Affiliation(s)
- Guy Cohen
- The Raymond and Beverley Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel
- School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel
| | - Michael Galperin
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
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4
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Hong J. Analyzing scanning tunneling spectroscopy for Fe-based superconductors and extracting sample density of states. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:375602. [PMID: 31163407 DOI: 10.1088/1361-648x/ab26fb] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We extract the density of states (DOS) from the scanning tunneling spectroscopy data for Ba1-x K x Fe2As2 superconductor. The obtained sample DOS is composed of two ordinary s-wave types from the band at [Formula: see text] point and a linear-like DOS within the s-wave gap from the band at M point in the Brillouin zone, and is consistent with the corresponding data from angle-resolved photoemission spectroscopy. We clarify that the major peak of the tunneling conductance is not related to the DOS but is rather the effect of nonequilibrium coherent tunneling including all coherent spins in the tip and sample.
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Affiliation(s)
- Jongbae Hong
- Research Institute of Basic Sciences, Incheon National University, Yeonsu-gu, Incheon 22012, Republic of Korea
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5
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Sorantin ME, Fugger DM, Dorda A, von der Linden W, Arrigoni E. Auxiliary master equation approach within stochastic wave functions: Application to the interacting resonant level model. Phys Rev E 2019; 99:043303. [PMID: 31108647 DOI: 10.1103/physreve.99.043303] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2018] [Indexed: 06/09/2023]
Abstract
We present further developments of the auxiliary master equation approach (AMEA), a numerical method to simulate many-body quantum systems in as well as out of equilibrium and apply it to the interacting resonant level model to benchmark the new developments. In particular, our results are obtained by employing the stochastic wave functions method to solve the auxiliary open quantum system arising within AMEA. This development allows us to reach extremely low wall times for the calculation of correlation functions with respect to previous implementations of AMEA. An additional significant improvement is obtained by extrapolating a series of results obtained by increasing the number of auxiliary bath sites, N_{B}, used within the auxiliary open quantum system formally to the limit of N_{B}→∞. Results for the current-voltage characteristics and for equilibrium correlation functions are compared with the one obtained by exact and matrix-product states-based approaches. Further, we complement this benchmark by the presentation of spectral functions for higher temperatures where we find different behaviors around zero frequency depending on the hybridization strength.
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Affiliation(s)
- Max E Sorantin
- Institute of Theoretical and Computational Physics, Graz University of Technology, 8010 Graz, Austria
| | - Delia M Fugger
- Institute of Theoretical and Computational Physics, Graz University of Technology, 8010 Graz, Austria
| | - Antonius Dorda
- Institute of Theoretical and Computational Physics, Graz University of Technology, 8010 Graz, Austria
| | - Wolfgang von der Linden
- Institute of Theoretical and Computational Physics, Graz University of Technology, 8010 Graz, Austria
| | - Enrico Arrigoni
- Institute of Theoretical and Computational Physics, Graz University of Technology, 8010 Graz, Austria
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6
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Nonequilibrium Thermodynamics and Steady State Density Matrix for Quantum Open Systems. ENTROPY 2017. [DOI: 10.3390/e19040158] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
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7
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Wang H, Thoss M. Employing an interaction picture to remove artificial correlations in multilayer multiconfiguration time-dependent Hartree simulations. J Chem Phys 2016; 145:164105. [DOI: 10.1063/1.4965712] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Haobin Wang
- Department of Chemistry, University of Colorado Denver, Denver, Colorado 80217-3364, USA
| | - Michael Thoss
- Institute for Theoretical Physics and Interdisciplinary Center for Molecular Materials, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7/B2, D-91058, Germany
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8
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Antipov AE, Dong Q, Gull E. Voltage Quench Dynamics of a Kondo System. PHYSICAL REVIEW LETTERS 2016; 116:036801. [PMID: 26849606 DOI: 10.1103/physrevlett.116.036801] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2015] [Indexed: 06/05/2023]
Abstract
We examine the dynamics of a correlated quantum dot in the mixed valence regime. We perform numerically exact calculations of the current after a quantum quench from equilibrium by rapidly applying a bias voltage in a wide range of initial temperatures. The current exhibits short equilibration times and saturates upon the decrease of temperature at all times, indicating Kondo behavior both in the transient regime and in the steady state. The time-dependent current saturation temperature connects the equilibrium Kondo temperature to a substantially increased value at voltages outside of the linear response. These signatures are directly observable by experiments in the time domain.
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Affiliation(s)
- Andrey E Antipov
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Qiaoyuan Dong
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Emanuel Gull
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
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9
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Ness H. Nonequilibrium density matrix in quantum open systems: generalization for simultaneous heat and charge steady-state transport. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:062119. [PMID: 25615056 DOI: 10.1103/physreve.90.062119] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2014] [Indexed: 06/04/2023]
Abstract
We suggest a generalization of the expression of the nonequilibrium (NE) density matrix obtained by Hershfield's method for the cases where both heat and charge steady-state currents are present in a quantum open system. The finite-size quantum system, connected to two temperature and particle reservoirs, is driven out of equilibrium by the presence of both a temperature gradient and a chemical potential gradient between the two reservoirs. We show that the NE density matrix is given by a generalized Gibbs-like ensemble and is in full agreement with the general results of the McLennan-Zubarev nonequilibrium ensembles. The extra nonequilibrium terms are related to the entropy production in the system and characterize the fluxes of heat and particle. An explicit example, for the lowest-order expansion, is provide for a model system of noninteracting fermions.
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Affiliation(s)
- H Ness
- Department of Physics, Faculty of Natural and Mathematical Sciences, King's College London, Strand, London WC2R 2LS, United Kingdom
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Cohen G, Gull E, Reichman DR, Millis AJ. Green's functions from real-time bold-line Monte Carlo calculations: spectral properties of the nonequilibrium Anderson impurity model. PHYSICAL REVIEW LETTERS 2014; 112:146802. [PMID: 24766001 DOI: 10.1103/physrevlett.112.146802] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2013] [Indexed: 06/03/2023]
Abstract
The nonequilibrium spectral properties of the Anderson impurity model with a chemical potential bias are investigated within a numerically exact real-time quantum Monte Carlo formalism. The two-time correlation function is computed in a form suitable for nonequilibrium dynamical mean field calculations. Additionally, the evolution of the model's spectral properties are simulated in an alternative representation, defined by a hypothetical but experimentally realizable weakly coupled auxiliary lead. The voltage splitting of the Kondo peak is confirmed and the dynamics of its formation after a coupling or gate quench are studied. This representation is shown to contain additional information about the dot's population dynamics. Further, we show that the voltage-dependent differential conductance gives a reasonable qualitative estimate of the equilibrium spectral function, but significant qualitative differences are found including incorrect trends and spurious temperature dependent effects.
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Affiliation(s)
- Guy Cohen
- Department of Chemistry, Columbia University, New York, New York 10027, USA and Department of Physics, Columbia University, New York, New York 10027, USA
| | - Emanuel Gull
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - David R Reichman
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | - Andrew J Millis
- Department of Physics, Columbia University, New York, New York 10027, USA
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11
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Zheng X, Yan Y, Di Ventra M. Kondo memory in driven strongly correlated quantum dots. PHYSICAL REVIEW LETTERS 2013; 111:086601. [PMID: 24010458 DOI: 10.1103/physrevlett.111.086601] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2013] [Indexed: 06/02/2023]
Abstract
We investigate the real-time current response of strongly correlated quantum dot systems under sinusoidal driving voltages. By means of an accurate hierarchical equations of motion approach, we demonstrate the presence of prominent memory effects induced by the Kondo resonance on the real-time current response. These memory effects appear as distinctive hysteresis line shapes and self-crossing features in the dynamic current-voltage characteristics, with concomitant excitation of odd-number overtones. They emerge as a cooperative effect of quantum coherence-due to inductive behavior-and electron correlations-due to the Kondo resonance. We also show the suppression of memory effects and the transition to classical behavior as a function of temperature. All these phenomena can be observed in experiments and may lead to novel quantum memory applications.
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Affiliation(s)
- Xiao Zheng
- Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
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12
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Ness H. Nonequilibrium density matrix for quantum transport: Hershfield approach as a McLennan-Zubarev form of the statistical operator. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:022121. [PMID: 24032789 DOI: 10.1103/physreve.88.022121] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2013] [Indexed: 06/02/2023]
Abstract
In this paper, we formally demonstrate that the nonequilibrium density matrix developed by Hershfield for the steady state has the form of a McLennan-Zubarev nonequilibrium ensemble. The correction term in this pseudoequilibrium Gibbs-like ensemble is directly related to the entropy production in the quantum open system. The fact that both methods state that a nonequilibrium steady state can be mapped onto a pseudoequilibrium, permits us to develop nonequilibrium quantities from formal expressions equivalent to the equilibrium case. We provide an example: the derivation of a nonequilibrium distribution function for the electron population in a scattering region in the context of quantum transport.
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Affiliation(s)
- H Ness
- Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom
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13
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Wang H, Thoss M. Multilayer Multiconfiguration Time-Dependent Hartree Study of Vibrationally Coupled Electron Transport Using the Scattering-State Representation. J Phys Chem A 2013; 117:7431-41. [DOI: 10.1021/jp401464b] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Affiliation(s)
- Haobin Wang
- Department of Chemistry and Biochemistry, MSC 3C, New Mexico State University,
Las Cruces, New Mexico 88003, United States, and Beijing Computational Science Research Center, No. 3 He-Qing
Road, Hai-Dian District, Beijing 100084, P.R. China
| | - Michael Thoss
- Institute for Theoretical Physics and Interdisciplinary
Center for Molecular Materials, Friedrich-Alexander-Universität, Erlangen-Nürnberg, Staudtstrasse 7/B2, D-91058, Germany
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14
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Arrigoni E, Knap M, von der Linden W. Nonequilibrium dynamical mean-field theory: an auxiliary quantum master equation approach. PHYSICAL REVIEW LETTERS 2013; 110:086403. [PMID: 23473180 DOI: 10.1103/physrevlett.110.086403] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2012] [Indexed: 06/01/2023]
Abstract
We introduce a versatile method to compute electronic steady-state properties of strongly correlated extended quantum systems out of equilibrium. The approach is based on dynamical mean-field theory (DMFT), in which the original system is mapped onto an auxiliary nonequilibrium impurity problem imbedded in a Markovian environment. The steady-state Green's function of the auxiliary system is solved by full diagonalization of the corresponding Lindblad equation. The approach can be regarded as the nontrivial extension of the exact-diagonalization-based DMFT to the nonequilibrium case. As a first application, we consider an interacting Hubbard layer attached to two metallic leads and present results for the steady-state current and the nonequilibrium density of states.
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Affiliation(s)
- Enrico Arrigoni
- Institute of Theoretical and Computational Physics, Graz University of Technology, 8010 Graz, Austria.
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15
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Yi J, Kim S, Um J, Hwang SY, Go A, Jeon GS. Effective projection theory in a correlated electron system. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:485604. [PMID: 21406753 DOI: 10.1088/0953-8984/22/48/485604] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We propose an efficient method for nonperturbative calculation of Green's function in a correlated electron system. The key idea of the method is to project out irrelevant operators having zero norm in the ground state, which we refer to as effective projection theory. We apply the method to a mesoscopic Anderson model and show that for a given wavefunction ansatz, equations of motion can be closed only by relevant operators, allowing easy calculation of the zero-temperature Green's function. It turns out that the resulting Green's functions reproduce exact limits of both weak and strong interactions. The accuracy is also verified for small systems by comparison with exact diagonalization results, revealing that effective projection theory captures the essential correlated features in the entire regime of interactions.
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Affiliation(s)
- Juyeon Yi
- Department of Physics, Pusan National University, Busan, Korea
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Dirks A, Werner P, Jarrell M, Pruschke T. Continuous-time quantum Monte Carlo and maximum entropy approach to an imaginary-time formulation of strongly correlated steady-state transport. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:026701. [PMID: 20866934 DOI: 10.1103/physreve.82.026701] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2010] [Revised: 07/12/2010] [Indexed: 05/29/2023]
Abstract
Recently, Han and Heary [Phys. Rev. Lett. 99, 236808 (2007)] proposed an approach to steady-state quantum transport through mesoscopic structures, which maps the nonequilibrium problem onto a family of auxiliary quantum impurity systems subject to imaginary voltages. We employ continuous-time quantum Monte-Carlo solvers to calculate accurate imaginary time data for the auxiliary models. The spectral function is obtained from a maximum entropy analytical continuation in both Matsubara frequency and complexified voltage. To enable the analytical continuation we construct a kernel which is compatible with the analytical structure of the theory. While it remains a formidable task to extract reliable spectral functions from this unbiased procedure, particularly for large voltages, our results indicate that the method in principle yields results in agreement with those obtained by other methods.
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Affiliation(s)
- Andreas Dirks
- Department of Physics, University of Göttingen, D-37077 Göttingen, Germany
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Andergassen S, Meden V, Schoeller H, Splettstoesser J, Wegewijs MR. Charge transport through single molecules, quantum dots and quantum wires. NANOTECHNOLOGY 2010; 21:272001. [PMID: 20571187 DOI: 10.1088/0957-4484/21/27/272001] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
We review recent progress in the theoretical description of correlation and quantum fluctuation phenomena in charge transport through single molecules, quantum dots and quantum wires. Various physical phenomena are addressed, relating to cotunneling, pair-tunneling, adiabatic quantum pumping, charge and spin fluctuations, and inhomogeneous Luttinger liquids. We review theoretical many-body methods to treat correlation effects, quantum fluctuations, non-equilibrium physics, and the time evolution into the stationary state of complex nanoelectronic systems.
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Affiliation(s)
- S Andergassen
- Institut für Theoretische Physik A, RWTH Aachen, 52056 Aachen, Germany
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18
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Joura AV, Freericks JK, Pruschke T. Steady-state nonequilibrium density of States of driven strongly correlated lattice models in infinite dimensions. PHYSICAL REVIEW LETTERS 2008; 101:196401. [PMID: 19113287 DOI: 10.1103/physrevlett.101.196401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2008] [Revised: 10/06/2008] [Indexed: 05/27/2023]
Abstract
An exact formalism for calculating the retarded and advanced Green's functions of strongly correlated lattice models in a uniform electric field is derived within dynamical mean-field theory. To illustrate the method, we solve for the nonequilibrium density of states of the Hubbard model in both the metallic and Mott-insulating phases at half-filling (with an arbitrary strength electric field) by employing the approximate numerical renormalization group as the impurity solver. This general approach can be applied to any strongly correlated lattice model in the limit of large dimensions.
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Affiliation(s)
- A V Joura
- Department of Physics, Georgetown University, 37th and O Sts. NW, Washington, DC 20057, USA
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Anders FB. Steady-state currents through nanodevices: a scattering-states numerical renormalization-group approach to open quantum systems. PHYSICAL REVIEW LETTERS 2008; 101:066804. [PMID: 18764489 DOI: 10.1103/physrevlett.101.066804] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2008] [Indexed: 05/26/2023]
Abstract
We propose a numerical renormalization group (NRG) approach to steady-state currents through nanodevices. A discretization of the scattering-states continuum ensures the correct boundary condition for an open quantum system. We introduce two degenerate Wilson chains for current carrying left- and right-moving electrons reflecting time-reversal symmetry in the absence of a finite bias V. We employ the time-dependent NRG to evolve the known steady-state density operator for a noninteracting junction into the density operator of the fully interacting nanodevice at finite bias. We calculate the differential conductance as function of V, T, and the external magnetic field.
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Affiliation(s)
- Frithjof B Anders
- Institut für Theoretische Physik, Universität Bremen, P.O. Box 330 440, D-28334 Bremen, Germany
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