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Nuclear Physics B - Proceedings Supplements

A many-body approach to Hamiltonian lattice gauge field theories

R. F. Bishop, Yang Xian

Published Apr 1, 1994• 2 citations
Publisher
DOI
10.1016/0920-5632(94)90521-5

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Lattice gauge theories (LGTs) are one of the most fundamental subjects in many-body physics, and has recently attracted considerable research interests in quantum simulations.Here we experimentally investigate the emergent Z 2 gauge invariance in a 1D superconducting circuit with 10 transmon qubits.By precisely adjusting staggered longitudinal and transverse fields to each qubit, we construct an effective Hamiltonian containing anLGT and gauge-broken terms.The corresponding matter sector can exhibit a localization, and there also exists a 3-qubit operator, of which the expectation value can retain nonzero for a long time in low-energy regimes.The above localization can be regarded as the confinement of matter fields, and the 3-body operator is the Z 2 gauge generator.These experimental results demonstrate that, despite the absence of gauge structure in the effective Hamiltonian, Z 2 gauge invariance can still emerge in low-energy regimes.Our work provides a method for both theoretically and experimentally studying the rich physics in quantum many-body systems with emergent gauge invariance.
Abstract We study the Hamiltonian lattice Yang-Mills theory based on spin networks that provide a useful basis to represent the physical states satisfying the Gauss law constraints. We focus on SU(2) Yang-Mills theory in (2 + 1) dimensions. Following the string-net model, we introduce a regularization of the Kogut-Susskind Hamiltonian of lattice Yang-Mills theory based on the q deformation, which respects the (discretized) SU(2) gauge symmetry as quantum group, i.e., SU(2)k, and enables implementation of the lattice Yang-Mills theory both in classical and quantum algorithms by referring to those of the string-net model. Using the regularized Hamiltonian, we study quantum scars in a nonabelian gauge theory. Quantum scars are nonthermal energy eigenstates arising in the constrained quantum many-body systems. We find that quantum scars from zero modes, which have been found in abelian gauge theories arise even in a nonabelian gauge theory. We also show the spectrum of a single-plaquette model for SU(2)k and SU(3)k with naive cutoff and that based on the q-deformation to discuss cutoff dependence of the formulation.