Crystalline confinement

Abstract

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 pseudoGoldstone 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.

Partition-free approach to open quantum systems in harmonic environments: An exact stochastic Liouville equation

“…Parallel to this is the work of Stockburger, exactly deriving a stochastic Liouville-von Neumann (SLN) equation, and applying it to two-level systems [46]. Approaches based on influence functionals have also found use in the real time numerical simulations of dissipative systems [47][48][49][50][51][52][53]. With this corpus of techniques, path integrals (and specifically influence functionals) represent a powerful and flexible formalism that can be used to attack the problem of open quantum systems.…”

From quantum link models to D-theory: a resource efficient framework for the quantum simulation and computation of gauge theories

“…Most remarkably, quantum simulation experiments of quantum link models including matter fields using ultracold atomic gases in optical superlattices have already been performed successfully [41,42], with impressive control of the gauge symmetry. Numerous different aspects of (2 + 1)-d U(1) quantum link models have been investigated in [52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68].…”

“…Both phases are characterized by the spontaneous breakdown of lattice rotation invariance, and are qualitatively new 'nematic' confined phases. Similarly, on the square lattice there are 'crystalline' confined phases in which lattice translation invariance is spontaneously broken [53,54]. Both on the triangular and on the square lattice, the phase transition that separates the two bulk confined phases is characterized by a ring-shaped order parameter distribution indicating an emergent, approximate, global SO(2) symmetry, which is spontaneously broken.…”

Two-dimensional lattice gauge theories with superconducting quantum circuits

“…(2) is , and thus only contributes as a constant energy shift. In this case, a gauge invariant extension of the gauge field Hamiltonian can be considered, for example, of the form [47,48] where denotes the sum over all plaquettes. The first term (“kinetic energy”) inverts the direction of the electric flux around flippable plaquettes, while the second term (“potential energy”) favors the formation of flippable plaquettes.…”

“…Confinement is characterized by the energy of the electric flux strings that connect charge and anticharge, and whose energy is proportional to the string length. In quantum link and quantum dimer models the strings fractionalize into strands of electric flux [47,48] and [49] , respectively. Of specific interest in the context of quantum simulation are dynamical properties, such as the evolution after a quench [50] .…”