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arXiv:2204.06570 · PRX Quantum

Tuning the Topological θ -Angle in Cold-Atom Quantum Simulators of Gauge Theories

Jad C. Halimeh, Ian P. McCulloch, Bing Yang, Philipp Hauke

Published Nov 9, 2022• 53 citations
arXivHTMLPDF

Abstract

The topological θ-angle in gauge theories engenders a series of fundamental phenomena, including violations of charge-parity (CP) symmetry, dynamical topological transitions, and confinementdeconfinement transitions.At the same time, it poses major challenges for theoretical studies, as it implies a sign problem in numerical simulations.Analog quantum simulators open the promising prospect of treating quantum many-body systems with such topological terms, but, contrary to their digital counterparts, they have not yet demonstrated the capacity to control the θ-angle.Here, we demonstrate how a tunable topological θ-term can be added to a prototype theory with U(1) gauge symmetry, a discretized version of quantum electrodynamics in one spatial dimension.As we show, the model can be realized experimentally in a single-species Bose-Hubbard model in an optical superlattice with three different spatial periods, thus requiring only standard experimental resources.Through numerical calculations obtained from the timedependent density-matrix renormalization group method and exact diagonalization, we benchmark the model system, and illustrate how salient effects due to the θ-term can be observed.These include charge confinement, the weakening of quantum many-body scarring, as well as the disappearance of Coleman's phase transition due to explicit breaking of CP symmetry.This work opens the door towards studying the rich physics of topological gauge-theory terms in large-scale cold-atom quantum simulators.

DOI
10.1103/prxquantum.3.040316

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The topological θ-angle in gauge theories engenders a series of fundamental phenomena, including violations of charge-parity (CP) symmetry, dynamical topological transitions, and confinementdeconfinement transitions.At the same time, it poses major challenges for theoretical studies, as it implies a sign problem in numerical simulations.Analog quantum simulators open the promising prospect of treating quantum many-body systems with such topological terms, but, contrary to their digital counterparts, they have not yet demonstrated the capacity to control the θ-angle.Here, we demonstrate how a tunable topological θ-term can be added to a prototype theory with U(1) gauge symmetry, a discretized version of quantum electrodynamics in one spatial dimension.As we show, the model can be realized experimentally in a single-species Bose-Hubbard model in an optical superlattice with three different spatial periods, thus requiring only standard experimental resources.Through numerical calculations obtained from the timedependent density-matrix renormalization group method and exact diagonalization, we benchmark the model system, and illustrate how salient effects due to the θ-term can be observed.These include charge confinement, the weakening of quantum many-body scarring, as well as the disappearance of Coleman's phase transition due to explicit breaking of CP symmetry.This work opens the door towards studying the rich physics of topological gauge-theory terms in large-scale cold-atom quantum simulators.
The quantum simulation of gauge theories on synthetic quantum matter devices has gained a lot of traction in the last decade, making possible the observation of a range of exotic quantum many-body phenomena. In this work, we consider the spin- 1 / 2 quantum link formulation of 1 + 1 D quantum electrodynamics with a topological θ -angle, which can be used to tune a confinement-deconfinement transition. Exactly mapping this system onto a PXP model with mass and staggered magnetization terms, we show an intriguing interplay between confinement and the ergodicity-breaking paradigms of quantum many-body scarring and Hilbert-space fragmentation. We map out the rich dynamical phase diagram of this model, finding an ergodic phase at small values of the mass μ and confining potential χ , an emergent integrable phase for large μ , and a fragmented phase for large values of both parameters. We also show that the latter hosts resonances that lead to a vast array of effective models. We propose experimental probes of our findings, which can be directly accessed in current cold-atom setups.
We present a detailed study of the topological Schwinger model [Phys. Rev. D 99, 014503 (2019)], which describes (1+11+11+1) quantum electrodynamics of an Abelian U(1)U(1)U(1) gauge field coupled to a symmetry-protected topological matter sector, by means of a class of ZN{\mathbb{Z}}_{N}ZN​ lattice gauge theories. Employing density-matrix renormalization group techniques that exactly implement Gauss' law, we show that these models host a correlated topological phase for different values of NNN, where fermion correlations arise through interparticle interactions mediated by the gauge field. Moreover, by a careful finite-size scaling, we show that this phase is stable in the large-NNN limit and that the phase boundaries are in accordance with bosonization predictions of the U(1)U(1)U(1) topological Schwinger model. Our results demonstrate that ZN{\mathbb{Z}}_{N}ZN​ finite-dimensional gauge groups offer a practical route for an efficient classical simulation of equilibrium properties of electromagnetism with topological fermions. Additionally, we describe a scheme for the quantum simulation of a topological Schwinger model exploiting spin-changing collisions in boson-fermion mixtures of ultracold atoms in optical lattices. Although technically challenging, this quantum simulation would provide an alternative to classical density-matrix renormalization group techniques, providing also an efficient route to explore real-time nonequilibrium phenomena.
A major objective of the strong ongoing drive to realize quantum simulators of gauge theories is achieving the capability to probe collider-relevant physics on them. In this regard, a highly pertinent and sought-after application is the controlled collisions of elementary and composite particles, as well as the scattering processes in their wake. Here, we propose particle-collision experiments in a cold-atom quantum simulator for a 1 + 1 D (one spatial and one temporal dimension) U(1) lattice gauge theory with a tunable topological θ term, where we demonstrate an experimentally feasible protocol to impart momenta to elementary (anti)particles and their meson composites. We numerically benchmark the collisions of moving wave packets for both elementary and composite particles, uncovering a plethora of rich phenomena, such as oscillatory string dynamics in the wake of elementary (anti)particle collisions due to confinement. We also probe string inversion and entropy production processes across Coleman’s phase transition through far-from-equilibrium quenches. We further demonstrate how collisions of composite particles unveil their internal structure. Our work paves the way towards the experimental investigation of collision dynamics in state-of-the-art quantum simulators of gauge theories, and sets the stage for microscopic understanding of collider-relevant physics in these platforms. Published by the American Physical Society 2024
Aiming at a better understanding of anomalous and topological effects in gauge theories out of equilibrium, we study the real-time dynamics of a prototype model for CP violation, the massive Schwinger model with a θ term. We identify dynamical quantum phase transitions between different topological sectors that appear after sufficiently strong quenches of the θ parameter. Moreover, we establish a general dynamical topological order parameter, which can be accessed through fermion two-point correlators and, importantly, which can be applied for interacting theories. Enabled by this result, we show that the topological transitions persist beyond the weak-coupling regime. Finally, these effects can be observed with tabletop experiments based on existing cold-atom, superconducting-qubit, and trapped-ion technology. Our Letter thus presents a significant step towards quantum simulating topological and anomalous real-time phenomena relevant to nuclear and high-energy physics.
Abstract A major driver of quantum-simulator technology is the prospect of probing high-energy phenomena in synthetic quantum matter setups at a high level of control and tunability. Here, we propose an experimentally feasible realization of a large-scale 2 + 1D U(1) gauge theory with dynamical matter and gauge fields in a cold-atom quantum simulator with spinless bosons. We present the full mapping of the corresponding Gauss’s law onto the bosonic computational basis. We then show that the target gauge theory can be faithfully realized and stabilized by an emergent gauge protection term in a two-dimensional single-species Bose–Hubbard optical Lieb superlattice with two spatial periods along either direction, thereby requiring only moderate experimental resources already available in current cold-atom setups. Using infinite matrix product states, we calculate numerical benchmarks for adiabatic sweeps and global quench dynamics that further confirm the fidelity of the mapping. Our work brings quantum simulators of gauge theories a significant step forward in terms of investigating particle physics in higher spatial dimensions, and is readily implementable in existing cold-atom platforms.
Quantum technologies offer the prospect to efficiently simulate sign-problem afflicted regimes in lattice field theory, such as the presence of topological terms, chemical potentials, and out-of-equilibrium dynamics. In this work, we derive the (3+1)D(3+1)\mathrm{D}(3+1)D topological $\ensuremath{\theta}$-term for Abelian and non-Abelian lattice gauge theories in the Hamiltonian formulation, paving the way toward Hamiltonian-based simulations of such terms on quantum and classical computers. We further study numerically the zero-temperature phase structure of a (3+1)D(3+1)\mathrm{D}(3+1)D U(1) lattice gauge theory with the $\ensuremath{\theta}$-term via exact diagonalization for a single periodic cube. In the strong coupling regime, our results suggest the occurrence of a phase transition at constant values of $\ensuremath{\theta}$, as indicated by an avoided level crossing and abrupt changes in the plaquette expectation value, the electric energy density, and the topological charge density. These results could in principle be cross-checked by the recently developed (3+1)D(3+1)\mathrm{D}(3+1)D tensor network methods and quantum simulations, once sufficient resources become available.