The (2 + 1)-d U (1) quantum link model is a gauge theory, amenable to quantum simulation, with a spontaneously broken S O (2) symmetry emerging at a quantum phase transition. Its low-energy physics is described by a (2 + 1)-d R P (1) effective field theory, perturbed by an S O (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.
The (2 + 1)-d U (1) quantum link model is a gauge theory, amenable to quantum simulation, with a spontaneously broken S O (2) symmetry emerging at a quantum phase transition. Its low-energy physics is described by a (2 + 1)-d R P (1) effective field theory, perturbed by an S O (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.
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 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) 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.
Continuous quantum phase transitions beyond the conventional paradigm of fluctuations of a symmetry-breaking order parameter are challenging for theory.These phase transitions often involve emergent deconfined gauge fields at the critical points as demonstrated in phase transitions between different broken-symmetry states of 2 þ 1-dimensional quantum magnets, as well as those between symmetry-protected topological (SPT) phases.In this paper, we present several examples of deconfined quantum critical points between SPT phases in 3 þ 1-D for both bosonic and fermionic systems.These critical theories can be formulated as non-Abelian gauge theories either in the infrared-free regime or in the conformal window when they flow to the Banks-Zaks fixed points.We explicitly demonstrate several interesting quantum critical phenomena.We describe situations in which the same phase transition allows for multiple universality classes controlled by distinct fixed points.We exhibit the possibility-which we dub "unnecessary quantum critical points"-of stable generic continuous phase transitions within the same phase.We present examples of interaction-driven, band-theory-forbidden, continuous phase transitions between two distinct band insulators.The understanding we develop leads us to suggest an interesting possible 3 þ 1-D field theory duality between SUð2Þ gauge theory coupled to one massless adjoint Dirac fermion and the theory of a single massless Dirac fermion augmented by a decoupled topological field theory.
<!--HTML-->Quantum link models provide an extension of Wilson's lattice gauge theory in which the link variables have operator-valued entries. For example, in a U(1) quantum link model the link variables are raising and lowering operators of quantum spins that belong to a link-based SU(2) embedding algebra. For non-Abelian SU(N), Spin(N), or Sp(N) quantum link models, the embedding algebras are SU(2N), Spin(2N), and Sp(2N), respectively. In contrast to Wilson's framework, quantum link models can be realized in a finite-dimensional link Hilbert space corresponding to a representation of the embedding algebra. This is well suited for a resource efficient implementation of quantum link models in quantum simulation experiments. The quantum link dynamics can be embodied with a finite number of well-controlled states of ultra-cold matter, including atoms in an optical lattice, ions in a trap, or quantum circuits. For example, using dual variables, a densely encoded quantum circuit has recently been constructed for a (2+1)-d U(1) quantum link model on a triangular lattice that shows qualitatively new nematic phases with rich confining dynamics. Quantum spins and quantum links are discrete quantum variables which give rise to collective low-energy excitations. In (2+1)-d, SU(N) quantum spins give rise to massless Goldstone bosons which undergo dimensional reduction to (1+1)-d asymptotically free CP(N-1) models. This can be realized in quantum simulation experiments with alkaline-earth atoms in an optical lattice. In (3+1)-d, Abelian quantum links give rise to massless photons which undergo dimensional reduction to (2+1)-d confining U(1) gauge theory, which can be embodied with spin-ice. In (4+1)-d, non-Abelian quantum links give rise to massless gluons which undergo dimensional reduction to (3+1)-d Yang-Mills theory. Quarks are naturally included as domain wall fermions. The dimensional reduction of discrete quantum variables defines D-theory, in which quantum field theories emerge from a minimal set of degrees of freedom, thus enabling resource efficient implementations in quantum simulation experiments. D-theory provides a concrete vision how to realize the ultimate long-term goal of quantum simulating QCD.
We explore the ground-state physics of two-dimensional spin-1/2 U(1) quantum link models, one of the simplest nontrivial lattice gauge theories with fermionic matter within experimental reach for quantum simulations. Whereas in the large mass limit we observe Neél-like vortex-antivortex and striped crystalline phases, for small masses there is a transition from the striped phases into a disordered phase whose properties resemble those at the Rokhsar-Kivelson point of the quantum dimer model. This phase is characterized on ladders by boundary Haldane-like properties, such as vanishing parity and finite string ordering. Moreover, from studies of the string tension between gauge charges, we find that, whereas the striped phases are confined, the novel disordered phase present clear indications of being deconfined. Our results open exciting perspectives of studying highly nontrivial physics in quantum simulators, such as spin-liquid behavior and confinement-deconfinement transitions, without the need of explicitly engineering plaquette terms.
Investigating novel manifestations of quantum criticality is central to modern theoretical condensed matter physics. Here, the authors unveil the exotic quantum phase diagram of a two-dimensional system of single-component fermions, minimally coupled to dynamical Ising gauge fields. With state-of-the-art numerical methods, the authors detect a robust quantum critical line, where gauge confinement and translation symmetry breaking occur simultaneously. The authors conjecture a u(1) deconfined criticality scenario, and propose a corresponding low-energy effective field theory of the exotic quantum critical point.
Using quantum Monte Carlo simulations, we study a series of models of fermions coupled to quantum Ising spins on a square lattice with N flavors of fermions per site for N ¼ 1, 2, and 3.The models have an extensive number of conserved quantities but are not integrable, and they have rather rich phase diagrams consisting of several exotic phases and phase transitions that lie beyond the Landau-Ginzburg paradigm.In particular, one of the prominent phases for N > 1 corresponds to 2N gapless Dirac fermions coupled to an emergent Z 2 gauge field in its deconfined phase.However, unlike a conventional Z 2 gauge theory, we do not impose "Gauss's Law" by hand; instead, it emerges because of spontaneous symmetry breaking.Correspondingly, unlike a conventional Z 2 gauge theory in two spatial dimensions, our models have a finite-temperature phase transition associated with the melting of the order parameter that dynamically imposes the Gauss's law constraint at zero temperature.By tuning a parameter, the deconfined phase undergoes a transition into a short-range entangled phase, which corresponds to Néel antiferromagnet or superconductor for N ¼ 2 and a valence-bond solid for N ¼ 3. Furthermore, for N ¼ 3, the valence-bond solid further undergoes a transition to a Néel phase consistent with the deconfined quantum critical phenomenon studied earlier in the context of quantum magnets.