[Paper Review] Approximating Lattice Gauge Theories on Superconducting Circuits: Quantum Phase Transition and Quench Dynamics

Zi-Yong Ge, Rui-Zhen Huang+2 more|arXiv (Cornell University)|Sep 29, 2020

Quantum many-body systems41 references4 citations

TL;DR

This paper proposes a superconducting quantum circuit implementation of $ζ_2$ lattice gauge theory (LGT) with an effective gauge-broken term, using matrix product state methods to study ground state properties and quench dynamics. It reveals a quantum phase transition from a disordered to a translational symmetry-breaking phase, with an emergent approximate Gaussian law in the ordered phase and dynamical signatures of symmetry breaking and confinement.

ABSTRACT

We propose an implementation to approximate $\mathbb{Z}_2$ lattice gauge theory (LGT) on superconducting quantum circuits, where the effective theory is a mixture of a LGT and a gauge-broken term. Using matrix product state based methods, both the ground state properties and quench dynamics are systematically investigated. With an increase of the transverse (electric) field, the system displays a quantum phase transition from a disordered phase to a translational symmetry breaking phase. In the ordered phase, an approximate Gaussian law of the $\mathbb{Z}_2$ LGT emerges in the ground state. Moreover, to shed light on the experiments, we also study the quench dynamics, where there is a dynamical signature of the spontaneous translational symmetry breaking. The spreading of the single particle of matter degree is diffusive under the weak transverse field, while it is ballistic with small velocity for the strong field. Furthermore, due to the existence of an approximate Gaussian law under the strong transverse field, the matter degree can also exhibit a confinement which leads to a strong suppression of the nearest-neighbor hopping. Our results pave the way for simulating the LGT on superconducting circuits, including the quantum phase transition and quench dynamics.

Motivation & Objective

• To develop a scalable superconducting quantum circuit platform for simulating $ζ_2$ lattice gauge theories (LGTs), which are classically intractable.
• To investigate the ground state phase diagram of the effective LGT Hamiltonian, particularly the emergence of spontaneous translational symmetry breaking.
• To explore quench dynamics in the system, focusing on the spreading of matter particles and dynamical signatures of symmetry breaking.
• To examine the role of the transverse (electric) field in inducing confinement and modifying particle transport behavior.
• To establish a bridge between theoretical LGT models and experimental realization on superconducting quantum processors.

Proposed method

• The authors map the $ζ_2$ LGT onto a superconducting circuit architecture, introducing an effective Hamiltonian that includes both gauge-theory and gauge-broken terms.
• Matrix product state (MPS)-based numerical methods are employed to efficiently simulate the many-body ground state and time evolution under quench protocols.
• The transverse field strength is varied to tune the system across a quantum phase transition, with the order parameter monitored to detect symmetry breaking.
• The dynamics of a single matter particle's spreading is analyzed to distinguish between diffusive and ballistic transport regimes.
• The emergence of an approximate Gaussian law in the ordered phase is identified through correlation and field distribution analysis.
• Confinement effects are probed by observing the suppression of nearest-neighbor hopping in the strong-field regime.

Experimental results

Research questions

• RQ1 How does increasing the transverse field induce a quantum phase transition in the $ζ_2$ lattice gauge theory on superconducting circuits?
• RQ2 What dynamical signatures emerge during quench dynamics that indicate spontaneous translational symmetry breaking?
• RQ3 How does the nature of matter particle transport change from diffusive to ballistic as the transverse field increases?
• RQ4 Under what conditions does an approximate Gaussian law for the gauge field emerge in the ground state?
• RQ5 To what extent does the strong transverse field lead to confinement of matter degrees of freedom?

Key findings

• The system undergoes a quantum phase transition from a disordered phase to a translational symmetry-breaking phase as the transverse field increases.
• In the ordered phase, an approximate Gaussian distribution emerges for the gauge field, indicating a stable, coherent configuration.
• Single-particle matter dynamics are diffusive under weak transverse fields but become ballistic with small velocity under strong fields.
• The strong transverse field induces effective confinement, suppressing nearest-neighbor hopping of matter degrees of freedom.
• The dynamical evolution reveals clear signatures of spontaneous translational symmetry breaking during quench processes.
• The results demonstrate the feasibility of simulating complex LGT phenomena, including phase transitions and confinement, on superconducting quantum circuits.