Matrix product purifications for canonical ensembles and quantum number distributions

Abstract

Matrix product purifications (MPPs) are a very efficient tool for the simulation of strongly correlated quantum many-body systems at finite temperatures. When a system features symmetries, these can be used to reduce computation costs substantially. It is straightforward to compute an MPP of a grand-canonical ensemble, also when symmetries are exploited. This paper provides and demonstrates methods for the efficient computation of MPPs of canonical ensembles under utilization of symmetries. Furthermore, we present a scheme for the evaluation of global quantum number distributions using matrix product density operators (MPDOs). We provide exact matrix product representations for canonical infinite-temperature states, and discuss how they can be constructed alternatively by applying matrix product operators to vacuum-type states or by using entangler Hamiltonians. A demonstration of the techniques for Heisenberg spin-1/2 chains explains why the difference in the energy densities of canonical and grand-canonical ensembles decays as 1/L.

9 pages, 5 figures; minor improvements, published version

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• Optimized Lie-Trotter-Suzuki decompositions for two and three non-commuting terms
• Quantum chaos and ensemble inequivalence of quantum long-range Ising chains
• Dynamical properties of the $S=\frac{1}{2}$ random Heisenberg chain
• Exceptional points in the one-dimensional Hubbard model
• Symmetric minimally entangled typical thermal states for canonical and grand-canonical ensembles
• One-dimensional quantum systems at finite temperatures can be simulated efficiently on classical computers
• Finite-temperature optical conductivity with density-matrix renormalization group methods for the Holstein polaron and bipolaron with dispersive phonons
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• Cooling schemes for two-component fermions in layered optical lattices
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• Low-energy excitations and transport functions of the one-dimensional Kondo insulator
• Light-induced phase transitions in vanadium dioxide: a tensor network study
• Quantum Joule Expansion of One-Dimensional Systems
• Thermal and optical conductivity in the Holstein model at half filling and at finite temperature in the Luttinger-liquid and charge-density-wave regime
• Thermal DMRG for highly frustrated quantum spin chains: a user perspective
• Emergence of topological states in relaxation dynamics of interacting bosons
• Minimal one-dimensional model of bad metal behavior from fast particle-hole scattering