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arXiv:2210.03062

Studying chirality imbalance with quantum algorithms

Alexander M. Czajka, Zhong-Bo Kang, Yuxuan Tee, F. Zhao

Published Oct 6, 2022• 1 citation
arXivHTMLPDF

Abstract

To describe the chiral magnetic effect, the chiral chemical potential $μ_5$ is introduced to imitate the impact of topological charge changing transitions in the quark-gluon plasma under the influence of an external magnetic field. We employ the (1+1) dimensional Nambu-Jona-Lasinio (NJL) model to study the chiral phase structure and chirality charge density of strongly interacting matter with finite chiral chemical potential $μ_5$ in a quantum simulator. By performing the Quantum imaginary time evolution (QITE) algorithm, we simulate the (1+1) dimensional NJL model on the lattice at various temperature $T$ and chemical potentials $μ$, $μ_5$ and find that the quantum simulations are in good agreement with analytical calculations as well as exact diagonalization of the lattice Hamiltonian.

DOI
10.48550/arxiv.2210.03062

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To describe the chiral magnetic effect, the chiral chemical potential μ5μ_5μ5​ is introduced to imitate the impact of topological charge changing transitions in the quark-gluon plasma under the influence of an external magnetic field. We employ the (1+1) dimensional Nambu-Jona-Lasinio (NJL) model to study the chiral phase structure and chirality charge density of strongly interacting matter with finite chiral chemical potential μ5μ_5μ5​ in a quantum simulator. By performing the Quantum imaginary time evolution (QITE) algorithm, we simulate the (1+1) dimensional NJL model on the lattice at various temperature TTT and chemical potentials μμμ, μ5μ_5μ5​ and find that the quantum simulations are in good agreement with analytical calculations as well as exact diagonalization of the lattice Hamiltonian.
Abstract The Nambu–Jona-Lasinio (NJL) model has been widely studied for investigating the chiral phase structure of strongly interacting matter. The study of the thermodynamics of field theories within the framework of Lattice Field Theory is limited by the sign problem, which prevents Monte Carlo evaluation of the functional integral at a finite chemical potential. Using the quantum imaginary time evolution (QITE) algorithm, we construct a quantum simulation for the (1 + 1) dimensional NJL model at finite temperature and finite chemical potential. We observe consistency among digital quantum simulation, exact diagonalization and analytical solution, indicating further applications of quantum computing in simulating QCD thermodynamics.
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 implement a variational quantum algorithm to investigate the chiral condensate in a 1 + 1 dimensional SU(2) non-Abelian gauge theory. The algorithm is evaluated using a proposed Monte Carlo sampling method, which allows the extension to large qubit systems. The obtained results through quantum simulations on classical and actual quantum hardware are in good agreement with exact diagonalization of the lattice Hamiltonian, revealing the phenomena of chiral symmetry breaking and restoration as functions of both temperature and chemical potential. Our findings underscore the potential of near-term quantum computing for exploring QCD systems at finite temperature and density in non-Abelian gauge theories.
In this paper we study a (1+11+11+1)-dimensional version of the famous Nambu--Jona-Lasinio model of quantum chromodynamics (QCD2) both at zero and at finite baryon density. We use nonperturbative techniques (non-Abelian bosonization and the truncated conformal spectrum approach). When the baryon chemical potential, $\ensuremath{\mu}$, is zero, we describe the formation of fermion three-quark (nucleons and $\mathrm{\ensuremath{\Delta}}$ baryons) and boson (two-quark mesons, six-quark deuterons) bound states. We also study at $\ensuremath{\mu}=0$ the formation of a topologically nontrivial phase. When the chemical potential exceeds the critical value and a finite baryon density appears, the model has a rich phase diagram which includes phases with a density wave and superfluid quasi-long-range (QLR) order, as well as a phase of a baryon Tomonaga-Luttinger liquid (strange metal). The QLR order results in either a condensation of scalar mesons (the density wave) or six-quark bound states (deuterons).
The chiral magnetic and chiral separation effects-quantum-anomaly-induced electric current and chiral current along an external magnetic field in parity-odd quark-gluon plasma-have received intense studies in the community of heavy-ion collision physics. We show that analogous effects occur in rotating trapped Fermi gases with Weyl-Zeeman spin-orbit coupling where the rotation plays the role of an external magnetic field. These effects can induce a mass quadrupole in the atomic cloud along the rotation axis which may be tested in future experiments. Our results suggest that the spin-orbit coupled atomic gases are potential simulators of the chiral magnetic and separation effects.