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Vaezi MS, Negari AR, Moharramipour A, Vaezi A. Amelioration for the Sign Problem: An Adiabatic Quantum Monte Carlo Algorithm. PHYSICAL REVIEW LETTERS 2021; 127:217003. [PMID: 34860094 DOI: 10.1103/physrevlett.127.217003] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2020] [Revised: 03/29/2021] [Accepted: 10/11/2021] [Indexed: 06/13/2023]
Abstract
We introduce the adiabatic quantum Monte Carlo (AQMC) method, where we gradually crank up the interaction strength, as an amelioration of the sign problem. It is motivated by the adiabatic theorem and will approach the true ground state if the evolution time is long enough. We demonstrate that the AQMC algorithm enhances the average sign exponentially such that low enough temperatures can be accessed and ground-state properties probed. It is a controlled approximation that satisfies the variational theorem and provides an upper bound for the ground-state energy. We first benchmark the AQMC algorithm vis-à-vis the undoped Hubbard model on the square lattice which is known to be sign-problem-free within the conventional quantum Monte Carlo formalism. Next, we test the AQMC algorithm against the density-matrix-renormalization-group approach for the doped four-leg ladder Hubbard model and demonstrate its remarkable accuracy. As a nontrivial example, we apply our method to the Hubbard model at p=1/8 doping for a 16×8 system and discuss its ground-state properties. We finally utilize our method and demonstrate the emergence of U(1)_{2}∼SU(2)_{1} topological order in a strongly correlated Chern insulator.
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Affiliation(s)
- Mohammad-Sadegh Vaezi
- Pasargad Institute for Advanced Innovative Solutions (PIAIS), Tehran 19916-33361, Iran
| | - Amir-Reza Negari
- Department of Physics, Sharif University of Technology, Tehran 14588-89694, Iran
| | - Amin Moharramipour
- Department of Physics, Sharif University of Technology, Tehran 14588-89694, Iran
| | - Abolhassan Vaezi
- Department of Physics, Sharif University of Technology, Tehran 14588-89694, Iran
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Yang S, Ying T, Li W, Yang J, Sun X, Li X. Quantum Monte Carlo study of the Hubbard model with next-nearest-neighbor hopping t': pairing and magnetism. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:115601. [PMID: 33316793 DOI: 10.1088/1361-648x/abd33a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Using the finite-temperature determinant quantum Monte Carlo (DQMC) algorithm, we study the pairing symmetries of the Hubbard Hamiltonian with next-nearest-neighbor (NNN) hopping t' on square lattices. By varying the value of t', we find that the d-wave pairing is suppressed by the onset of t', while the p + ip-wave pairing tends to emerge for low electron density and t' around -0.7. Together with the calculation of the anti-ferromagnetic and ferromagnetic spin correlation function, we explore the relationship between anti-ferromagnetic order and the d-wave pairing symmetry, and the relationship between ferromagnetic order and the p + ip-wave pairing symmetry. Our results may be useful for the exploration of the mechanism of the electron pairing symmetries, and for the realization of the exotic p + ip-wave superconductivity.
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Affiliation(s)
- Shuhui Yang
- School of Physics, Harbin Institute of Technology, Harbin, 150001, People's Republic of China
| | - Tao Ying
- School of Physics, Harbin Institute of Technology, Harbin, 150001, People's Republic of China
| | - Weiqi Li
- School of Physics, Harbin Institute of Technology, Harbin, 150001, People's Republic of China
| | - Jianqun Yang
- School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, People's Republic of China
| | - Xiudong Sun
- School of Physics, Harbin Institute of Technology, Harbin, 150001, People's Republic of China
| | - Xingji Li
- School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, People's Republic of China
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White AF, Chan GKL. A Time-Dependent Formulation of Coupled-Cluster Theory for Many-Fermion Systems at Finite Temperature. J Chem Theory Comput 2018; 14:5690-5700. [DOI: 10.1021/acs.jctc.8b00773] [Citation(s) in RCA: 39] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Alec F. White
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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Ayral T, Vučičević J, Parcollet O. Fierz Convergence Criterion: A Controlled Approach to Strongly Interacting Systems with Small Embedded Clusters. PHYSICAL REVIEW LETTERS 2017; 119:166401. [PMID: 29099214 DOI: 10.1103/physrevlett.119.166401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2017] [Indexed: 06/07/2023]
Abstract
We present an embedded-cluster method, based on the triply irreducible local expansion formalism. It turns the Fierz ambiguity, inherent to approaches based on a bosonic decoupling of local fermionic interactions, into a convergence criterion. It is based on the approximation of the three-leg vertex by a coarse-grained vertex computed from a self-consistently determined cluster impurity model. The computed self-energies are, by construction, continuous functions of momentum. We show that, in three interaction and doping regimes of the two-dimensional Hubbard model, self-energies obtained with clusters of size four only are very close to numerically exact benchmark results. We show that the Fierz parameter, which parametrizes the freedom in the Hubbard-Stratonovich decoupling, can be used as a quality control parameter. By contrast, the GW+extended dynamical mean field theory approximation with four cluster sites is shown to yield good results only in the weak-coupling regime and for a particular decoupling. Finally, we show that the vertex has spatially nonlocal components only at low Matsubara frequencies.
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Affiliation(s)
- Thomas Ayral
- Physics and Astronomy Department, Rutgers University, Piscataway, New Jersey 08854, USA
- Institut de Physique Théorique (IPhT), CEA, CNRS, UMR 3681, 91191 Gif-sur-Yvette, France
| | - Jaksa Vučičević
- Institut de Physique Théorique (IPhT), CEA, CNRS, UMR 3681, 91191 Gif-sur-Yvette, France
- Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia
| | - Olivier Parcollet
- Institut de Physique Théorique (IPhT), CEA, CNRS, UMR 3681, 91191 Gif-sur-Yvette, France
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Carlström J. Spin-charge transformation of lattice fermion models: duality approach for diagrammatic simulation of strongly correlated systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:385602. [PMID: 28682299 DOI: 10.1088/1361-648x/aa7e1b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
I derive a dual description of lattice fermions, specifically focusing on the t-J and Hubbard models, that allow diagrammatic techniques to be employed efficiently in the strongly correlated regime, as well as for systems with a restricted Hilbert space. These constructions are based on spin-charge transformation, where the lattice fermions of the original model are mapped onto spins and spin-less fermions. This mapping can then be combined with Popov-Fedotov fermionisation, where the spins are mapped onto lattice fermions with imaginary chemical potential. The resulting models do not contain any large expansion parameters, even for strongly correlated systems. Also, they exhibit dramatically smaller corrections to the density matrix from nonlinear terms in the Hamiltonian. The combination of these two properties means that they can be addressed with diagrammatic methods, including simulation techniques based on stochastic sampling of diagrammatic expansions.
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Affiliation(s)
- Johan Carlström
- Department of Physics, University of Massachusetts, Amherst MA 01003, United States of America. Department of Physics, Stockholm University, 106 91 Stockholm, Sweden
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Abstract
In the traditional Bardeen–Cooper–Schrieffer theory of superconductivity, the amplitude for the propagation of a pair of electrons with momentum k and −k has a log singularity as the temperature decreases. This so-called Cooper instability arises from the presence of an electron Fermi sea. It means that an attractive interaction, no matter how weak, will eventually lead to a pairing instability. However, in the pseudogap regime of the cuprate superconductors, where parts of the Fermi surface are destroyed, this log singularity is suppressed, raising the question of how pairing occurs in the absence of a Fermi sea. Here we report Hubbard model numerical results and the analysis of angular-resolved photoemission experiments on a cuprate superconductor. In contrast to the traditional theory, we find that in the pseudogap regime the pairing instability arises from an increase in the strength of the spin–fluctuation pairing interaction as the temperature decreases rather than the Cooper log instability. Pairing interaction appears at room temperature in traditional superconductors with a Cooper instability in the Fermi sea. Here, Maier et al. report that in the pseudogap phase of cuprate, where this instability is absent, superconductivity arises from an increase in the strength of the spin fluctuation pairing interaction as the temperature decreases.
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Murakami Y, Werner P, Tsuji N, Aoki H. Supersolid phase accompanied by a quantum critical point in the intermediate coupling regime of the Holstein model. PHYSICAL REVIEW LETTERS 2014; 113:266404. [PMID: 25615362 DOI: 10.1103/physrevlett.113.266404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2014] [Indexed: 06/04/2023]
Abstract
We reveal that electron-phonon systems described by the Holstein model on a bipartite lattice exhibit, away from half filling, a supersolid (SS) phase characterized by coexisting charge order (CO) and superconductivity (SC), and an accompanying quantum critical point (QCP). The SS phase, demonstrated by the dynamical mean-field theory with a quantum Monte Carlo impurity solver, emerges in the intermediate-coupling regime, where the peak of the Tc dome is located and the metal-insulator crossover occurs. On the other hand, in the weak- and strong-coupling regimes the CO-SC boundary is of first order with no intervening SS phases. The QCP is associated with the continuous transition from SS to SC and characterized by a reentrant behavior of the SS around it. We further show that the SS-SC transition is hallmarked by diverging charge fluctuations and a kink (peak) in the superfluid density.
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Affiliation(s)
- Yuta Murakami
- Department of Physics, University of Tokyo, Hongo, Tokyo 113-0033, Japan
| | - Philipp Werner
- Department of Physics, University of Fribourg, 1700 Fribourg, Switzerland
| | - Naoto Tsuji
- Department of Physics, University of Tokyo, Hongo, Tokyo 113-0033, Japan
| | - Hideo Aoki
- Department of Physics, University of Tokyo, Hongo, Tokyo 113-0033, Japan
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Gull E, Parcollet O, Millis AJ. Superconductivity and the pseudogap in the two-dimensional Hubbard model. PHYSICAL REVIEW LETTERS 2013; 110:216405. [PMID: 23745902 DOI: 10.1103/physrevlett.110.216405] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2012] [Indexed: 06/02/2023]
Abstract
Recently developed numerical methods have enabled the explicit construction of the superconducting state of the Hubbard model of strongly correlated electrons in parameter regimes where the model also exhibits a pseudogap and a Mott insulating phase. d(x(2)-y(2)) symmetry superconductivity is found to occur in proximity to the Mott insulator, but separated from it by a pseudogapped nonsuperconducting phase. The superconducting transition temperature and order parameter amplitude are found to be maximal at the onset of the normal-state pseudogap. The emergence of superconductivity from the normal state pseudogap leads to a decrease in the excitation gap. All of these features are consistent with the observed behavior of the copper-oxide superconductors.
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Affiliation(s)
- Emanuel Gull
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
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Merino J, Gunnarsson O. Origin of the pseudogap in cuprate superconductors from quantum cluster theories. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:052201. [PMID: 23264461 DOI: 10.1088/0953-8984/25/5/052201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We analyze the origin of the pseudogap present in cuprate superconductors. We elucidate the mechanism of pseudogap formation close to the Mott localization within the dynamical cluster approach (DCA) to the Hubbard model. As the Coulomb interaction is increased, cluster-bath Kondo states are destroyed and a nondegenerate bound cluster state is formed, leading to a pseudogap. This occurs first at the antinodal point due to its weaker coupling to the bath, explaining the momentum dependence of the pseudogap. We find that the character of the pseudogap is related to breaking d-wave pairs.
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Affiliation(s)
- J Merino
- Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, Madrid E-28049, Spain.
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Lin N, Gull E, Millis AJ. Two-particle response in cluster dynamical mean-field theory: formalism and application to the Raman response of high-temperature superconductors. PHYSICAL REVIEW LETTERS 2012; 109:106401. [PMID: 23005307 DOI: 10.1103/physrevlett.109.106401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2012] [Indexed: 06/01/2023]
Abstract
A method is presented for the unbiased numerical computation of two-particle response functions of correlated electron materials via a solution of the dynamical mean-field equations in the presence of a perturbing field. The power of the method is demonstrated via a computation of the Raman B(1g) and B(2g) scattering intensities of the two-dimensional Hubbard model in parameter regimes believed to be relevant to high-temperature superconductivity. The theory reproduces the "two-magnon" peak characteristic of the Raman intensity of insulating parent compounds of high-T(c) copper oxide superconductors, and shows how it evolves to a quasiparticle response, as carriers are added. The method can be applied in any situation where a solution of equilibrium dynamical mean-field equations is feasible.
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Affiliation(s)
- Nan Lin
- Department of Physics, Columbia University, New York, New York 10027, USA
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Fotso H, Yang S, Chen K, Pathak S, Moreno J, Jarrell M, Mikelsons K, Khatami E, Galanakis D. Dynamical Cluster Approximation. SPRINGER SERIES IN SOLID-STATE SCIENCES 2012. [DOI: 10.1007/978-3-642-21831-6_9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
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Giovannetti G, Ortix C, Marsman M, Capone M, van den Brink J, Lorenzana J. Proximity of iron pnictide superconductors to a quantum tricritical point. Nat Commun 2011; 2:398. [PMID: 21772269 PMCID: PMC3160143 DOI: 10.1038/ncomms1407] [Citation(s) in RCA: 68] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2011] [Accepted: 06/20/2011] [Indexed: 11/13/2022] Open
Abstract
In several materials, unconventional superconductivity appears nearby a quantum phase transition where long-range magnetic order vanishes as a function of a control parameter like charge doping, pressure or magnetic field. The nature of the quantum phase transition is of key relevance, because continuous transitions are expected to favour superconductivity, due to strong fluctuations. Discontinuous transitions, on the other hand, are not expected to have a similar role. Here we determine the nature of the magnetic quantum phase transition, which occurs as a function of doping, in the iron-based superconductor LaFeAsO(1-x)F(x). We use constrained density functional calculations that provide ab initio coefficients for a Landau order parameter analysis. The outcome is intriguing, as this material turns out to be remarkably close to a quantum tricritical point, where the transition changes from continuous to discontinuous, and several susceptibilities diverge simultaneously. We discuss the consequences for superconductivity and the phase diagram.
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Affiliation(s)
- Gianluca Giovannetti
- Dipartimento di Fisica, Università di Roma 'La Sapienza', P. Aldo Moro 2, Roma 00185, Italy
- Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, Dipartimento di Fisica, Università di Roma 'La Sapienza', P. Aldo Moro 2, Roma 00185, Italy
- Istituto Officina dei Materiali, Consiglio Nazionale delle Ricerche, SISSA, Via Bonomea 265, 34136 Trieste, Italy
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), Condensed Matter Sector, Via Bonomea 265, Trieste 34136, SISSA, Via Bonomea 265, 34136 Trieste, Italy
| | - Carmine Ortix
- Institute for Theoretical Solid State Physics, IFW-Dresden, PF 270116, Dresden 01171, Germany
| | - Martijn Marsman
- Faculty of Physics and Center for Computational Materials Science, University Vienna, Sensengasse 8/12, Vienna A-1090, Austria
| | - Massimo Capone
- Dipartimento di Fisica, Università di Roma 'La Sapienza', P. Aldo Moro 2, Roma 00185, Italy
- Istituto Officina dei Materiali, Consiglio Nazionale delle Ricerche, SISSA, Via Bonomea 265, 34136 Trieste, Italy
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), Condensed Matter Sector, Via Bonomea 265, Trieste 34136, SISSA, Via Bonomea 265, 34136 Trieste, Italy
| | - Jeroen van den Brink
- Institute for Theoretical Solid State Physics, IFW-Dresden, PF 270116, Dresden 01171, Germany
| | - José Lorenzana
- Dipartimento di Fisica, Università di Roma 'La Sapienza', P. Aldo Moro 2, Roma 00185, Italy
- Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, Dipartimento di Fisica, Università di Roma 'La Sapienza', P. Aldo Moro 2, Roma 00185, Italy
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