Thermal Pure Quantum Matrix Product States Recovering a Volume Law Entanglement

Abstract

We propose a way to construct a thermal pure quantum matrix product state (TPQ-MPS) that can simulate finite temperature quantum many-body systems with a minimal numerical cost comparable to the matrix product algorithm for the ground state. The MPS was originally designed for the wave function with area-law entanglement. However, by attaching the auxiliary sites to the edges of the random matrix product state, we find that the degree of entanglement is automatically tuned so as to recover the volume law of the entanglement entropy that characterizes the TPQ state. The finite temperature physical quantities of the transverse Ising and the spin-1/2 Heisenberg chains evaluated by a TPQ-MPS show excellent agreement even for bond dimension $\sim 10$-$20$ with those of the exact results.

5 pages, 3 figures

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• Energy-filtered random-phase states as microcanonical thermal pure quantum states
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• Spin Seebeck Effect of Triangular-lattice Spin Supersolid
• Low-temperature Gibbs states with tensor networks
• Thermal pure matrix product state in two dimensions: tracking thermal equilibrium from paramagnet down to the Kitaev honeycomb spin liquid state
• Evaluating thermal expectation values by almost ideal sampling with Trotter gates
• Quantum many-body simulation of finite-temperature systems with sampling a series expansion of a quantum imaginary-time evolution
• Sample complexity of matrix product states at finite temperature
• Truncation error in series expansions linking microcanonical and canonical ensembles
• The statistical mechanics and machine learning of the $\alpha$-Rényi ensemble
• Specific heat and susceptibility of S=1/2 antiferromagnets on square, triangular, and kagome lattices
• Geometrically Taming Dynamical Entanglement Growth in Purified Quantum States