The (2 + 1)-d U(1) quantum link model masquerading as deconfined criticality

Abstract

The (2 + 1)-d U (1) quantum link model is a gauge theory, amenable to quantum simulation, with a spontaneously broken SO(2) symmetry emerging at a quantum phase transition. Its 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. At the quantum phase transition, the model mimics some features of deconfined quantum criticality, but remains linearly confining. Deconfinement only sets in at high temperature.Quantum link models (QLMs) are lattice gauge theories formulated in terms of discrete quantum degrees of freedom. U (1) and SU (2) QLMs were first constructed by Horn in 1981 [1], and further investigated in [2]. In [3] QLMs were introduced as an alternative nonperturbative regularization of Abelian and non-Abelian gauge theories, in which ordinary gauge fields emerge dynamically from the dimensional reduction of discrete quantum link variables. Dimensional reduction of discrete variables is a generic phenomenon in asymptotically free theories, which gives rise to the D-theory formulation of quantum field theory [4]. In the D-theory formulation of 4-d Quantum Chromodynamics (QCD), the confining gluon field emerges by dimensional reduction from a deconfined Coulomb phase of a (4 + 1)-d SU (3) QLM [5]. Chiral quarks arise naturally as domain wall fermions located at the two 4-d sides of a (4 + 1)-d slab. The (2 + 1)-d U (1) QLM has also been investigated in the context of quantum spin liquids [6]. With staggered background charges ±1, it is equivalent to a quantum dimer model [7][8][9]. Furthermore, Kitaev's toric code [10] is a Z(2) QLM. In contrast to Wilson's lattice gauge theory [11], QLMs have a finite-dimensional Hilbert space per link, which makes them ideally suited for the construction of atomic quantum simulators for dynamical Abelian [12][13][14][15][16] and non-Abelian gauge theories [17][18][19][20]. A long-term goal of this research is to quantum simulate QCD in the D-theory formulation with ultracold matter, in order to address the real-time evolution of strongly interacting systems in nuclear and particle physics, as well as their dynamics at non-zero baryon density.In this paper, we investigate the (2+1)-d U (1) QLM, in order to demonstrate that, despite its structural simplicity, it displays highly non-trivial dynamics, and thus is ideally suited to demonstrate the power of gauge theory quantum simulators. We consider the model with a plaquette coupling J and a Rokhsar-Kivelson (RK) coupling λ. The phase diagram is sketched in Fig.1. At zero temperature, the model is confining for λ < 1. At finite temperature T , it has a deconfinement phase transition above which there is a massless mode transforming non-trivially under the U (1) center symmetry. Due to the Mermin- FIG. 1. [Color online]Schematic sketch of the λ-T phase diagram. The insets indicate the location of the peaks in the probability distribution of the order p...

Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories

“…In fact, the quantum dimer model has the same Hamiltonian as the quantum link model, but replaces the usual Gauss law by a staggered background of static charges ±1. It turns out that the quantum phase transition masquerades as a deconfined quantum critical point, at which an approximate spontaneously broken global SO(2) symmetry with an almost massless pseudo-Goldstone boson emerges dynamically [84]. However, since the Goldstone boson is not exactly massless, it cannot be interpreted as a dual photon, and the theory remains confining at the quantum phase transition, albeit with a rather small string tension.…”

Towards quantum simulating QCD

“…In fact, several severe sign or complex action problems have been solved with the meron-cluster algorithm [2,3,4] or with the fermion bag approach [5,6,7]. Even the real-time evolution of a large strongly coupled quantum spin system, whose dynamics is entirely driven by measurements, has recently been simulated successfully with a cluster algorithm [8].…”

Crystalline confinement

“…In this article, we report on a study of the (2 + 1)-dimensional U(1) quantum link model and show that, despite its structural simplicity, it has a very rich phase diagram [22]. This model has exotic confining phases where the confining string joining a static charge-anti-charge pair splits into distinct fractionalized flux 1 2 strands.…”

“…The U(1) Gauss law constraint is implemented in the cluster building rules, which ensure that only the configurations with net zero charge at the vertices are generated. The details of the dualization procedure as well as the algorithm will be presented elsewhere [23]. We define a 2-component order parameter (M A , M B ), associated with the even and odd sublattices A and B, to characterize the different phases of the model.…”

“…The two phases realized in the QLM both have four peaks in the order parameter distribution p(M A , M B ), and are separated by a weak first order phase transition. In addition, there is an intermediate phase with eight peaks, separated from the other phases by second order phase transitions [22]. …”