Continuous Matrix Product Operator Approach to Finite Temperature Quantum States

2020/04/30 by Wei Tang, Hong-Hao Tu, Lei Wang
Physics and Astronomy · #Ising model #Matrix multiplication #Matrix product state #Observable #Operator (biology) #Opinion Dynamics and Social Influence #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum many-body systems #Quantum mechanics #Statistical physics #Thermodynamic limit #cond-mat.stat-mech #cond-mat.str-el #physics.comp-ph

paper · pdf · doi:10.1103/physrevlett.125.170604

published as Phys. Rev. Lett. 125, 170604 (2020) · 4.5+6 pages, 3+6 figures, published version, code: https://github.com/TensorBFS/cMPO

openalex publication_date 2020/10/23 · arxiv created 2020/10/24 · arxiv updated 2020/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We present an algorithm for studying quantum systems at finite temperature using continuous matrix product operator representation. The approach handles both short-range and long-range interactions in the thermodynamic limit without incurring any time discretization error. Moreover, the approach provides direct access to physical observables including the specific heat, local susceptibility, and local spectral functions. After verifying the method using the prototypical quantum XXZ chains, we apply it to quantum Ising models with power-law decaying interactions and on the infinite cylinder, respectively. The approach offers predictions that are relevant to experiments in quantum simulators and the nuclear magnetic resonance spin-lattice relaxation rate.

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