1
|
Trung HQ, Yang B. Fractionalization and Dynamics of Anyons and Their Experimental Signatures in the ν=n+1/3 Fractional Quantum Hall State. PHYSICAL REVIEW LETTERS 2021; 127:046402. [PMID: 34355928 DOI: 10.1103/physrevlett.127.046402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2020] [Accepted: 06/29/2021] [Indexed: 06/13/2023]
Abstract
We show the low-lying excitations at filling factor ν=n+1/3 with realistic interactions can be understood as quantum fluids with "Gaffnian quasiholes" as the proper elementary degrees of freedom. Each Laughlin quasihole can thus be understood as a bound state of two Gaffnian quasiholes, which in the lowest Landau level (LLL) behaves like "partons" with "asymptotic freedom" mediated by neutral excitations acting as "gluons." Near the experimentally observed nematic FQH phase in higher LLs, quasiholes become weakly bound and can fractionalize with rich dynamical properties. By studying the effective interactions between quasiholes, we predict a finite temperature phase transition of the Laughlin quasiholes even when the Laughlin ground state remains incompressible, and derive relevant experimental conditions for its possible observations.
Collapse
Affiliation(s)
- Ha Quang Trung
- Division of Physics and Applied Physics, Nanyang Technological University, Singapore 637371
| | - Bo Yang
- Division of Physics and Applied Physics, Nanyang Technological University, Singapore 637371
- Institute of High Performance Computing, A*STAR, Singapore 138632
| |
Collapse
|
2
|
Yang B. Fractional Quantum Hall Effect from Frustration-Free Hamiltonians. PHYSICAL REVIEW LETTERS 2020; 125:176402. [PMID: 33156656 DOI: 10.1103/physrevlett.125.176402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2020] [Accepted: 09/24/2020] [Indexed: 05/06/2023]
Abstract
We show that there is an emergent lattice description for the continuous fractional quantum Hall (FQH) systems, with a generalized set of few-body coherent states. In particular, model Hamiltonians of the FQH effect (FQHE) are equivalent to the real-space von Neumann lattice of local projection operators imposed on a continuous system in the thermodynamic limit. It can be analytically derived that tuning local one-body potentials in such lattices amounts to the tuning of individual two- or few-body pseudopotentials. For some cases, we can realize pure few-body pseudopotentials important for stabilizing exotic non-Abelian topological phases. Thus, this new approach can potentially lead to the experimental realization of coveted non-Abelian quantum fluids including the Moore-Read state and the Fibonacci state. The reformulation of the FQHE as a sum of local projections opens up new paths for rigorously proving the incompressibility of microscopic Hamiltonians in the thermodynamic limit.
Collapse
Affiliation(s)
- Bo Yang
- Division of Physics and Applied Physics, Nanyang Technological University, Singapore 637371 and Institute of High Performance Computing, A*STAR, Singapore, 138632
| |
Collapse
|
3
|
Pires MA, Queirós SMD. Quantum walks with sequential aperiodic jumps. Phys Rev E 2020; 102:012104. [PMID: 32794977 DOI: 10.1103/physreve.102.012104] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2019] [Accepted: 06/03/2020] [Indexed: 11/07/2022]
Abstract
We analyze a set of discrete-time quantum walks for which the displacements on a chain follow binary aperiodic jumps according to three paradigmatic sequences: Fibonacci, Thue-Morse, and Rudin-Shapiro. We use a generalized Hadamard coin, C[over ̂]_{H}, as well as a generalized Fourier coin, C[over ̂]_{K}. We verify the QW experiences a slowdown of the wave packet spreading, σ^{2}(t)∼t^{α}, by the aperiodic jumps whose exponent, α, depends on the type of aperiodicity. Additional aperiodicity-induced effects also emerge, namely, (1) while the superdiffusive regime (1<α<2) is predominant, α displays an unusual sensibility with the type of coin operator where the more pronounced differences emerge for the Rudin-Shapiro and random protocols and (2) even though the angle θ of the coin operator is homogeneous in space and time, there is a nonmonotonic dependence of α with θ. Fingerprints of the aperiodicity in the hoppings are also found when distributional measures such as the Shannon and von Neumann entropies, the Inverse Participation Ratio, the Jensen-Shannon dissimilarity, and the kurtosis are computed, which allow assessing informational and delocalization features arising from these protocols and understanding the impact of linear and nonlinear correlations of the jump sequence in a quantum walk as well. Finally, we argue the spin-lattice entanglement is enhanced by aperiodic jumps.
Collapse
Affiliation(s)
- M A Pires
- Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro/RJ, Brazil
| | - S M Duarte Queirós
- Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro/RJ, Brazil.,National Institute of Science and Technology for Complex Systems, Brazil
| |
Collapse
|
4
|
Ghazaryan A, Graß T, Gullans MJ, Ghaemi P, Hafezi M. Light-Induced Fractional Quantum Hall Phases in Graphene. PHYSICAL REVIEW LETTERS 2017; 119:247403. [PMID: 29286754 DOI: 10.1103/physrevlett.119.247403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2017] [Indexed: 06/07/2023]
Abstract
We show how to realize two-component fractional quantum Hall phases in monolayer graphene by optically driving the system. A laser is tuned into resonance between two Landau levels, giving rise to an effective tunneling between these two synthetic layers. Remarkably, because of this coupling, the interlayer interaction at nonzero relative angular momentum can become dominant, resembling a hollow-core pseudopotential. In the weak tunneling regime, this interaction favors the formation of singlet states, as we explicitly show by numerical diagonalization, at fillings ν=1/2 and ν=2/3. We discuss possible candidate phases, including the Haldane-Rezayi phase, the interlayer Pfaffian phase, and a Fibonacci phase. This demonstrates that our method may pave the way towards the realization of non-Abelian phases, as well as the control of topological phase transitions, in graphene quantum Hall systems using optical fields and integrated photonic structures.
Collapse
Affiliation(s)
- Areg Ghazaryan
- Department of Physics, City College, City University of New York, New York, New York 10031, USA
| | - Tobias Graß
- Joint Quantum Institute, NIST and University of Maryland, College Park, Maryland 20742, USA
- Department of Physics, College Park, Maryland 20742, USA
| | - Michael J Gullans
- Joint Quantum Institute, NIST and University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA
| | - Pouyan Ghaemi
- Department of Physics, City College, City University of New York, New York, New York 10031, USA
- Department of Physics, Graduate Center, City University of New York, New York, New York 10016, USA
| | - Mohammad Hafezi
- Joint Quantum Institute, NIST and University of Maryland, College Park, Maryland 20742, USA
- Department of Physics, College Park, Maryland 20742, USA
- Department of Electrical Engineering and IREAP, University of Maryland, College Park, Maryland 20742, USA
| |
Collapse
|
5
|
Liu CR, Guo YW, Li ZJ, Li W, Chen Y. Realizing Tao-Thouless-like state in fractional quantum spin Hall effect. Sci Rep 2016; 6:33472. [PMID: 27649678 PMCID: PMC5030710 DOI: 10.1038/srep33472] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2016] [Accepted: 08/26/2016] [Indexed: 11/13/2022] Open
Abstract
The quest for exotic quantum states of matter has become one of the most challenging tasks in modern condensed matter communications. Interplay between topology and strong electron-electron interactions leads to lots of fascinating effects since the discovery of the fractional quantum Hall effect. Here, we theoretically study the Rashba-type spin-orbit coupling effect on a fractional quantum spin Hall system by means of finite size exact diagonalization. Numerical evidences from the ground degeneracies, states evolutions, entanglement spectra, and static structure factor calculations demonstrate that non-trivial fractional topological Tao-Thouless-like quantum state can be realized in the fractional quantum spin Hall effect in a thin torus geometric structure by tuning the strength of spin-orbit coupling. Furthermore, the experimental realization of the Tao-Thouless-like state as well as its evolution in optical lattices are also proposed. The importance of this prediction provides significant insight into the realization of exotic topological quantum states in optical lattice, and also opens a route for exploring the exotic quantum states in condensed matters in future.
Collapse
Affiliation(s)
- Chen-Rong Liu
- Department of Physics and State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China
| | - Yao-Wu Guo
- Department of Physics and State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China
| | - Zhuo-Jun Li
- State Key Laboratory of Functional Materials for Informatics and Shanghai Center for Superconductivity, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China.,CAS Center for Excellence in Superconducting Electronics, Shanghai 200050, China
| | - Wei Li
- State Key Laboratory of Functional Materials for Informatics and Shanghai Center for Superconductivity, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China.,CAS Center for Excellence in Superconducting Electronics, Shanghai 200050, China
| | - Yan Chen
- Department of Physics and State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China.,Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China
| |
Collapse
|
6
|
Barkeshli M. Charge 2e/3 Superconductivity and Topological Degeneracies without Localized Zero Modes in Bilayer Fractional Quantum Hall States. PHYSICAL REVIEW LETTERS 2016; 117:096803. [PMID: 27610873 DOI: 10.1103/physrevlett.117.096803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2016] [Indexed: 06/06/2023]
Abstract
It has been recently shown that non-Abelian defects with localized parafermion zero modes can arise in conventional Abelian fractional quantum Hall (FQH) states. Here we propose an alternate route to creating, manipulating, and measuring topologically protected degeneracies in bilayer FQH states coupled to superconductors, without the creation of localized parafermion zero modes. We focus mainly on electron-hole bilayers, with a ±1/3 Laughlin FQH state in each layer, with boundaries that are proximity coupled to a superconductor. We show that the superconductor induces charge 2e/3 quasiparticle-pair condensation at each boundary of the FQH state, and that this leads to (i) topologically protected degeneracies that can be measured through charge sensing experiments and (ii) a fractional charge 2e/3 ac Josephson effect. We demonstrate that an analog of non-Abelian braiding is possible, despite the absence of a localized zero mode. We discuss several practical advantages of this proposal over previous work, and also several generalizations.
Collapse
Affiliation(s)
- Maissam Barkeshli
- Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA
- Department of Physics, Condensed Matter Theory Center, University of Maryland, College Park, Maryland 20742, USA and Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA
| |
Collapse
|