scholarly journals Conductivity of disordered quantum lattice models at infinite temperature: Many-body localization

2010 ◽  
Vol 81 (22) ◽  
Author(s):  
Timothy C. Berkelbach ◽  
David R. Reichman
Keyword(s):  
Lattice Models ◽  
Many Body ◽  
Quantum Lattice ◽  
Infinite Temperature

scholarly journals Efficient and flexible approach to simulate low-dimensional quantum lattice models with large local Hilbert spaces

2021 ◽  
Vol 10 (3) ◽  
Author(s):  
Thomas Köhler ◽  
Jan Stolpp ◽  
Sebastian Paeckel
Keyword(s):  
Hilbert Spaces ◽  
Degrees Of Freedom ◽  
Lattice Models ◽  
Many Body ◽  
Lattice Systems ◽  
Quantum Lattice ◽  
Efficient Treatment ◽  
Half Filling ◽  
Low Dimensional ◽  
Reduced Density

Quantum lattice models with large local Hilbert spaces emerge across various fields in quantum many-body physics. Problems such as the interplay between fermions and phonons, the BCS-BEC crossover of interacting bosons, or decoherence in quantum simulators have been extensively studied both theoretically and experimentally. In recent years, tensor network methods have become one of the most successful tools to treat such lattice systems numerically. Nevertheless, systems with large local Hilbert spaces remain challenging. Here, we introduce a mapping that allows to construct artificial U(1)U(1) symmetries for any type of lattice model. Exploiting the generated symmetries, numerical expenses that are related to the local degrees of freedom decrease significantly. This allows for an efficient treatment of systems with large local dimensions. Further exploring this mapping, we reveal an intimate connection between the Schmidt values of the corresponding matrixproductstate representation and the singlesite reduced density matrix. Our findings motivate an intuitive physical picture of the truncations occurring in typical algorithms and we give bounds on the numerical complexity in comparison to standard methods that do not exploit such artificial symmetries. We demonstrate this new mapping, provide an implementation recipe for an existing code, and perform example calculations for the Holstein model at half filling. We studied systems with a very large number of lattice sites up to L=501L=501 while accounting for N_{\rm ph}=63 phonons per site with high precision in the CDW phase.

scholarly journals Numerical Linked-Cluster Approach to Quantum Lattice Models

2006 ◽  
Vol 97 (18) ◽  
Author(s):  
Marcos Rigol ◽  
Tyler Bryant ◽  
Rajiv R. P. Singh
Keyword(s):  
Lattice Models ◽  
Cluster Approach ◽  
Quantum Lattice

scholarly journals Series-expansion thermal tensor network approach for quantum lattice models

2017 ◽  
Vol 95 (16) ◽  
Author(s):  
Bin-Bin Chen ◽  
Yun-Jing Liu ◽  
Ziyu Chen ◽  
Wei Li
Keyword(s):  
Series Expansion ◽  
Lattice Models ◽  
Network Approach ◽  
Quantum Lattice ◽  
Tensor Network

scholarly journals Topology and Broken Symmetry in Floquet Systems

2020 ◽  
Vol 11 (1) ◽  
pp. 345-368 ◽  
Author(s):  
Fenner Harper ◽  
Rahul Roy ◽  
Mark S. Rudner ◽  
S.L. Sondhi
Keyword(s):  
Prima Facie ◽  
Particle Systems ◽  
Many Body ◽  
Nontrivial Behavior ◽  
Interacting Systems ◽  
State Of Affairs ◽  
Main Ideas ◽  
Nontrivial Topology ◽  
Infinite Temperature

Floquet systems are governed by periodic, time-dependent Hamiltonians. Prima facie they should absorb energy from the external drives involved in modulating their couplings and heat up to infinite temperature. However, this unhappy state of affairs can be avoided in many ways. Instead, as has become clear from much recent work, Floquet systems can exhibit a variety of nontrivial behavior—some of which is impossible in undriven systems. In this review, we describe the main ideas and themes of this work: novel Floquet drives that exhibit nontrivial topology in single-particle systems, the existence and classification of exotic Floquet drives in interacting systems, and the attendant notion of many-body Floquet phases and arguments for their stability to heating.

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