Deformed relativistic and nonrelativistic symmetries on canonical noncommutative spaces

We study the general deformed conformal-Poincare (Galilean) symmetries consistent with relativistic (nonrelativistic) canonical noncommutative spaces. In either case we obtain deformed generators, containing arbitrary free parameters, which close to yield new algebraic structures. We show that a particular choice of these parameters reproduces the undeformed algebra. The modified coproduct rules and the associated Hopf algebra are also obtained. Finally, we show that for the choice of parameters leading to the undeformed algebra, the deformations are represented by twist functions.Comment: 9 pages, LaTeX, shortened, version appearing in Phys. Rev.

The (2+1)-d U(1) Quantum Link Model Masquerading as Deconfined Criticality

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.Comment: 4.5 pages, 6 figure

Crystalline Confinement

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 $\mathbb{R}P(1)$ 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.Comment: Proceedings of the 31st International Symposium on Lattice Field Theory - LATTICE 201

Real-Time Simulation of Large Open Quantum Spin Systems driven by Measurements

We consider a large quantum system with spins $\frac{1}{2}$ whose dynamics is driven entirely by measurements of the total spin of spin pairs. This gives rise to a dissipative coupling to the environment. When one averages over the measurement results, the corresponding real-time path integral does not suffer from a sign problem. Using an efficient cluster algorithm, we study the real-time evolution of a 2-d Heisenberg antiferromagnet, which is driven to a disordered phase, either by sporadic measurements or by continuous monitoring described by Lindblad evolution.Comment: 5 pages, 7 figure

Phase space dynamics of overdamped quantum systems

The phase space dynamics of dissipative quantum systems in strongly condensed phase is considered. Based on the exact path integral approach it is shown that the Wigner transform of the reduced density matrix obeys a time evolution equation of Fokker-Planck type valid from high down to very low temperatures. The effect of quantum fluctuations is discussed and the accuracy of these findings is tested against exact data for a harmonic system.Comment: 7 pages, 2 figures, to appear in Euro. Phys. Let

From the SU(2)SU(2) Quantum Link Model on the Honeycomb Lattice to the Quantum Dimer Model on the Kagom\'e Lattice: Phase Transition and Fractionalized Flux Strings

We consider the $(2+1)$-d $SU(2)$ quantum link model on the honeycomb lattice and show that it is equivalent to a quantum dimer model on the Kagom\'e 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 non-trivially under the $\mathbb{Z}(2)$ center of the $SU(2)$ gauge group) are confined to each other by fractionalized strings with a delocalized $\mathbb{Z}(2)$ flux. The strands of the fractionalized flux strings are domain walls that separate distinct pinwheel phases. A second-order phase transition in the 3-d Ising universality class separates two confining phases; one with correlated pinwheel orientations, and the other with uncorrelated pinwheel orientations.Comment: 16 pages, 20 figures, 2 tables, two more relevant references and one short paragraph are adde

From the SU(2)SU(2) Quantum Link Model on the Honeycomb Lattice to the Quantum Dimer Model on the Kagom\'e Lattice: Phase Transition and Fractionalized Flux Strings

We consider the $(2+1)$-d $SU(2)$ quantum link model on the honeycomb lattice and show that it is equivalent to a quantum dimer model on the Kagom\'e 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 non-trivially under the $\mathbb{Z}(2)$ center of the $SU(2)$ gauge group) are confined to each other by fractionalized strings with a delocalized $\mathbb{Z}(2)$ flux. The strands of the fractionalized flux strings are domain walls that separate distinct pinwheel phases. A second-order phase transition in the 3-d Ising universality class separates two confining phases; one with correlated pinwheel orientations, and the other with uncorrelated pinwheel orientations.Comment: 16 pages, 20 figures, 2 tables, two more relevant references and one short paragraph are adde