Thermal States as Convex Combinations of Matrix Product States

Abstract

We study thermal states of strongly interacting quantum spin chains and prove that those can be represented in terms of convex combinations of matrix product states. Apart from revealing new features of the entanglement structure of Gibbs states our results provide a theoretical justification for the use of White's algorithm of minimally entangled typical thermal states. Furthermore, we shed new light on time dependent matrix product state algorithms which yield hydrodynamical descriptions of the underlying dynamics.

v3: 10 pages, 2 figures, final published version

References in corpus (14)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Matrix product states represent ground states faithfully
• Area laws in quantum systems: mutual information and correlations
• Aspects of generic entanglement
• Minimally Entangled Typical Thermal State Algorithms
• String order and symmetries in quantum spin lattices
• The power of quantum systems on a line
• Approximating Gibbs states of local Hamiltonians efficiently with PEPS
• Is efficiency of classical simulations of quantum dynamics related to integrability?
• Quantum Belief Propagation
• Quantum thermalization dynamics with Matrix-Product States
• Mixed s-sourcery: Building many-body states using bubbles of Nothing

Cited by in corpus (15)

• Many-body localization and delocalization in large quantum chains
• Improved thermal area law and quasi-linear time algorithm for quantum Gibbs states
• The Lyapunov Spectrum of Quantum Thermalisation
• Exponential clustering of bipartite quantum entanglement at arbitrary temperatures
• Analytic expressions for the steady-state current with finite extended reservoirs
• Collective Monte Carlo updates through tensor network renormalization
• Hamiltonian learning from time dynamics using variational algorithms
• Thermal Area Law in Long-Range Interacting Systems
• Connector tensor networks: a renormalization-type approach to quantum certification
• Markovian Matrix Product Density Operators : Efficient computation of global entropy
• Thermal Area Law for Lattice Bosons
• Constructing k-local parent Lindbladians for matrix product density operators
• Phase Transitions in the Classical Simulability of Open Quantum Systems
• Continuous matrix product operators for quantum fields
• Locally accurate tensor networks for thermal states and time evolution