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arXiv:2311.11616 · International Symposium on Lattice Field Theory (LATTICE)

Quantum Simulation of Finite Temperature Schwinger Model via Quantum Imaginary Time Evolution

Juan W. Pedersen, Etsuko Itou, Rong-Yang Sun, Seiji Yunoki

Published Dec 27, 2023• 6 citations
arXivHTMLPDF

Abstract

We study the Schwinger model at finite-temperature regime using a quantum-classical hybrid algorithm. The preparation of thermal state on quantum circuit presents significant challenges. To address this, we adopt the Thermal Pure Quantum (TPQ) state approach and apply the Quantum Imaginary Time Evolution (QITE) algorithm to implement the necessary imaginary time evolution. We first compute the chiral condensate in the massless Schwinger model, verifying its consistency with the analytical solution. We then simulate the massive Schwinger model with non-zero topological $\theta$-term to investigate the temperature and $\theta$-dependence of the chiral condensate. Our method works well even at non-zero $\theta$ regime, while the conventional lattice Monte Carlo method suffers from the sign problem in this system.

DOI
10.22323/1.453.0220

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In this study, we explore the real-time dynamics of the chiral magnetic effect (CME) at a finite temperature in the (1+1)-dimensional QED, the massive Schwinger model. By introducing a chiral chemical potential μ5μ_5μ5​ through a quench process, we drive the system out of equilibrium and analyze the induced vector currents and their evolution over time. The Hamiltonian is modified to include the time-dependent chiral chemical potential, thus allowing the investigation of the CME within a quantum computing framework. We employ the quantum imaginary time evolution (QITE) algorithm to study the thermal states, and utilize the Suzuki-Trotter decomposition for the real-time evolution. This study provides insights into the quantum simulation capabilities for modeling the CME and offers a pathway for studying chiral dynamics in low-dimensional quantum field theories.
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We investigate a quantum gauge theory at finite temperature and density using a variational algorithm for near-term quantum devices. We adapt βββ-VQE to evaluate thermal and quantum expectation values and study the phase diagram for massless Schwinger model along with the temperature and density. By compering the exact variational free energy, we find the variational algorithm work for T>0T>0T>0 and μ>0μ>0μ>0 for the Schwinger model. No significant volume dependence of the variational free energy is observed in μ/g∈[0,1.4]μ/g \in[0, 1.4]μ/g∈[0,1.4]. We calculate the chiral condensate and take the continuum extrapolation. As a result, we obtain qualitative picture of the phase diagram for massless Schwinger model.
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