Pure state thermodynamics with matrix product states

Abstract

We extend the formalism of pure state thermodynamics to matrix product states. In pure state thermodynamics finite temperature properties of quantum systems are derived without the need of statistical mechanics ensembles, but instead using typical properties of random pure states. We show that this formalism can be useful from the computational point of view when combined with tensor network algorithms. In particular, a recently introduced Monte Carlo algorithm is considered which samples matrix product states at random for the estimation of finite temperature observables. Here we characterize this algorithm as an $(\epsilon ,\delta )$-approximation scheme and we analytically show that sampling one single state is sufficient to obtain a very good estimation of finite temperature expectation values. These results provide a substantial computational improvement with respect to similar algorithms for one-dimensional quantum systems based on uniformly distributed pure states. The analytical calculations are numerically supported simulating finite temperature interacting spin systems of size up to 100 qubits.

20 pages, 3 figures; comments are welcome

References in corpus (11)

• The density-matrix renormalization group in the age of matrix product states
• Real time evolution using the density matrix renormalization group
• Foundation of Statistical Mechanics under experimentally realistic conditions
• Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
• Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space
• Canonical Thermal Pure Quantum State
• Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem
• Sequential Generation of Matrix-Product States in Cavity QED
• Sequentially generated states for the study of two dimensional systems
• Pure state quantum statistical mechanics and black holes
• Generalized quantum microcanonical ensemble from random matrix product states

Cited by in corpus (9)

• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• Pushing the limits of the eigenstate thermalization hypothesis towards mesoscopic quantum systems
• How much entanglement is needed to reduce the energy variance?
• Thermal Pure Quantum Matrix Product States Recovering a Volume Law Entanglement
• Equilibration on average in quantum processes with finite temporal resolution
• Purity of thermal mixed quantum states
• Microscopic electronic configurations after ultrafast magnetization dynamics
• Thermal Pure States for Systems with Antiunitary Symmetries and Their Tensor Network Representations
• Sample complexity of matrix product states at finite temperature