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Physical Review Research

Nematic confined phases in the U(1) quantum link model on a triangular lattice: Near-term quantum computations of string dynamics on a chip

Debasish Banerjee, Stephan Caspar, Fu-Jiun Jiang, J.-H. Peng, U.‐J. Wiese

Published Jun 1, 2022• 15 citations
Publisher

Abstract

The $\text{U}(1)$ quantum link model on the triangular lattice has two rotation-symmetry-breaking nematic confined phases. Static external charges are connected by confining strings consisting of individual strands with fractionalized electric flux. The two phases are separated by a weak first-order phase transition with an emergent, almost exact $\text{SO}(2)$ symmetry. We construct a quantum circuit on a chip to facilitate near-term quantum computations of the nontrivial string dynamics.

DOI
10.1103/physrevresearch.4.023176

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The U(1)\text{U}(1)U(1) quantum link model on the triangular lattice has two rotation-symmetry-breaking nematic confined phases. Static external charges are connected by confining strings consisting of individual strands with fractionalized electric flux. The two phases are separated by a weak first-order phase transition with an emergent, almost exact SO(2)\text{SO}(2)SO(2) symmetry. We construct a quantum circuit on a chip to facilitate near-term quantum computations of the nontrivial string dynamics.
Nematic Confined Phases in the U(1)U(1)U(1) Quantum Link Model on a Triangular Lattice: An Opportunity for Near-Term Quantum Computations of String Dynamics on a Chip
The U(1)U(1)U(1) quantum link model on the triangular lattice has two rotation-symmetry-breaking nematic confined phases. Static external charges are connected by confining strings consisting of individual strands with fractionalized electric flux. The two phases are separated by a weak first order phase transition with an emergent almost exact SO(2)SO(2)SO(2) symmetry. We construct a quantum circuit on a chip to facilitate near-term quantum computations of the non-trivial string dynamics.
We show that exotic phases arise in generalized lattice gauge theories known as quantum link models in which classical gauge fields are replaced by quantum operators.While these quantum models with discrete variables have a finite-dimensional Hilbert space per link, the continuous gauge symmetry is still exact.An efficient cluster algorithm is used to study these exotic phases.The (2 + 1)-d system is confining at zero temperature with a spontaneously broken translation symmetry.A crystalline phase exhibits confinement via multi-stranded strings between chargeanti-charge pairs.A phase transition between two distinct confined phases is weakly first order and has an emergent spontaneously broken approximate SO(2) global symmetry.The low-energy physics is described by a (2 + 1)-d RP(1) effective field theory, perturbed by a dangerously irrelevant SO(2) breaking operator, which prevents the interpretation of the emergent pseudo-Goldstone boson as a dual photon.This model is an ideal candidate to be implemented in quantum simulators to study phenomena that are not accessible using Monte Carlo simulations such as the real-time evolution of the confining string and the real-time dynamics of the pseudo-Goldstone boson.
We show that exotic phases arise in generalized lattice gauge theories known as quantum link models in which classical gauge fields are replaced by quantum operators. While these quantum models with discrete variables have a finite-dimensional Hilbert space per link, the continuous gauge symmetry is still exact. An efficient cluster algorithm is used to study these exotic phases. The (2+1)(2+1)(2+1)-d system is confining at zero temperature with a spontaneously broken translation symmetry. A crystalline phase exhibits confinement via multi-stranded strings between charge-anti-charge pairs. A phase transition between two distinct confined phases is weakly first order and has an emergent spontaneously broken approximate SO(2)SO(2)SO(2) global symmetry. The low-energy physics is described by a (2+1)(2+1)(2+1)-d RP(1)\mathbb{R}P(1)RP(1) effective field theory, perturbed by a dangerously irrelevant SO(2)SO(2)SO(2) breaking operator, which prevents the interpretation of the emergent pseudo-Goldstone boson as a dual photon. This model is an ideal candidate to be implemented in quantum simulators to study phenomena that are not accessible using Monte Carlo simulations such as the real-time evolution of the confining string and the real-time dynamics of the pseudo-Goldstone boson.
We consider the (2+1)(2+1)(2+1)-dimensional SU(2)SU(2)SU(2) quantum link model on the honeycomb lattice and show that it is equivalent to a quantum dimer model on the kagome lattice. The model has crystalline confined phases with spontaneously broken translation invariance associated with pinwheel order, which is investigated with either a Metropolis or an efficient cluster algorithm. External half-integer non-Abelian charges [which transform nontrivially under the Z(2)\mathbb{Z}(2)Z(2) center of the SU(2)SU(2)SU(2) gauge group] are confined to each other by fractionalized strings with a delocalized Z(2)\mathbb{Z}(2)Z(2) flux. The strands of the fractionalized flux strings are domain walls that separate distinct pinwheel phases. A second-order phase transition in the three-dimensional Ising universality class separates two confining phases: one with correlated pinwheel orientations, and the other with uncorrelated pinwheel orientations.
The (2+1)D U(1) pure gauge theory always exists in the confining phase, with strings of non-zero string tension giving a characteristic linear potential between static charges. This makes it a useful testing ground for quantum computing methods designed to study string dynamics of confining gauge theories. Here we implement a minimal U(1) quantum link model on a quantum computer with qubit degrees of freedom representing the dual height variables of the model. This facilitates an efficient realization of plaquette interactions and enables effective calculations of real-time dynamics that are inaccessible to traditional quantum Monte Carlo. A specifically tailored lattice geometry is chosen to match the heavy-hexagonal geometry of the IBM quantum hardware used here, minimizing non-adjacent qubit interactions. By performing quantum quenches from a simple initial string state, we probe the transverse quantum fluctuations of the string before it thermalizes. Our experimental results from digital quantum simulations, with up to 112 qubits, show good agreement with reference tensor-network calculations at short times and with thermal averages at long times. Near the phase transition, the quench dynamics exhibit large fluctuations of the initial string that extend across both spatial dimensions of the lattice. Nonetheless, our error-mitigated estimators from the quantum hardware also give accurate predictions in that regime, with noise-induced violations of local gauge symmetries comparable to finite-bond-dimension tensor-network results.
Lattice gauge theories (LGTs) describe fundamental interactions in particle physics. A central phenomenon in these theories is confinement, which binds quarks and antiquarks into hadrons through the formation of string-like flux tubes of gauge fields. Simulating confinement dynamics is a challenging task, but recent advances in quantum simulation are enabling the exploration of LGTs in regimes beyond the reach of classical computation. For analog devices, a major difficulty is the realization of strong plaquette interactions, which generate string fluctuations that can drive a roughening transition. Understanding string roughening -- where strong transversal functions lead to an effective restoration of translational symmetry at long distances -- is of central importance in the study of confinement. In this work, we show that string roughening emerges naturally in an analog Rydberg quantum simulator. We first map a triangular Rydberg array onto a (2+1)D U(1) LGT where plaquette terms appear as first-order processes. We study flux strings connecting static charges and demonstrate that, near a deconfined quantum critical point, the string exhibits logarithmic growth of its transverse width as the separation between charges increases, along with the universal Lüscher correction to the confining potential -- both signatures of string roughening. Finally, we investigate the real-time dynamics of an initially rigid string, observing large fluctuations after quenching into the roughening regime, as well as string breaking via particle-pair creation. Our results indicate that rough strings can be realized in experimentally accessible quantum simulators, opening the door to detailed studies of how strong fluctuations influence string-breaking dynamics.