A quantum topological phase transition at the microscopic level

We study a quantum phase transition between a phase which is topologically ordered and one which is not. We focus on a spin model, an extension of the toric code, for which we obtain the exact ground state for all values of the coupling constant that takes the system across the phase transition. We compute the entanglement and the topological entropy of the system as a function of this coupling constant, and show that the topological entropy remains constant all the way up to the critical point, and jumps to zero beyond it. Despite the jump in the topological entropy, the transition is second order as detected via any local observable.Comment: (13 pages, 4 figures) v2: updated references and acknowledgments; v3: final update (references) after publicatio

Dynamical obstruction in a constrained system and its realization in lattices of superconducting devices

Hard constraints imposed in statistical mechanics models can lead to interesting thermodynamical behaviors, but may at the same time raise obstructions in the thoroughfare to thermal equilibration. Here we study a variant of Baxter's 3-color model in which local interactions and defects are included, and discuss its connection to triangular arrays of Josephson junctions of superconductors and \textit{kagom\'e} networks of superconducting wires. The model is equivalent to an Ising model in a hexagonal lattice with the constraint that the magnetization of each hexagon is $\pm 6$ or 0. For ferromagnetic interactions, we find that the system is critical for a range of temperatures (critical line) that terminates when it undergoes an exotic first order phase transition with a jump from a zero magnetization state into the fully magnetized state at finite temperature. Dynamically, however, we find that the system becomes frozen into domains. The domain walls are made of perfectly straight segments, and domain growth appears frozen within the time scales studied with Monte Carlo simulations. This dynamical obstruction has its origin in the topology of the allowed reconfigurations in phase space, which consist of updates of closed loops of spins. As a consequence of the dynamical obstruction, there exists a dynamical temperature, lower than the (avoided) static critical temperature, at which the system is seen to jump from a ``supercooled liquid'' to a ``polycrystalline'' phase. In contrast, for antiferromagnetic interactions, we argue that the system orders for infinitesimal coupling because of the constraint, and we observe no interesting dynamical effects

Ten years of Nature Physics: The monopole movement

The monopole picture for spin ice offers a natural description for a confounding class of materials. A paper published in Nature Physics in 2009 applied it to study the dynamical properties of these systems -- sparking intense experimental and theoretical efforts in the years that followed.EPSRCThis is the author accepted manuscript. The final version is available from Nature Publishing Group via http://dx.doi.org/10.1038/nphys325

Distilling topological entropy from a single measurement of entanglement on projected systems

Entanglement measures find frequent application in the study of topologically ordered systems, where the presence of topological order is reflected in an additional contribution to the entanglement of the system. Obtaining this topological entropy from analytical calculations or numerical simulations is generally difficult due to the fact that it is an order one correction to leading terms that scale with the size of the system. In order to distil the topological entropy, one resorts to extrapolation as a function of system size, or to clever subtraction schemes that allow to cancel out the leading terms. Both approaches have the disadvantage of requiring multiple (accurate) calculations of the entanglement of the system. Here we propose a modification of conventional entanglement calculations that allows to obtain the topological entropy of a system from a single measurement of entanglement. In our approach, we replace the conventional trace over the degrees of freedom of a partition of the system with a projection onto a given state (which needs not be known). We show that a proper choice of partition and projective measurement allows to rid the entanglement measures of the typical boundary terms, thus exposing the topological contribution alone. We consider specifically the measures known as von Neumann entropy and entanglement negativity, and we discuss their application to both models that exhibit quantum as well as classical topological order.This work was supported by EPSRC Grant EP/K028960/1, and in part by the Helmholtz Virtual Institute “New States of Matter and Their Excitations” and by the EPSRC NetworkPlus on “Emergence and Physics far from Equilibrium”.This is the accepted manuscript version. The final version is available from APS at http://journals.aps.org/pra/abstract/10.1103/PhysRevA.89.042333

Two-dimensional topological order of kinetically constrained quantum particles

We investigate how imposing kinetic restrictions on quantum particles that would otherwise hop freely on a two-dimensional lattice can lead to topologically ordered states. The kinetically constrained models introduced here are derived as a generalization of strongly interacting particle systems in which hoppings are given by flux-lattice Hamiltonians and may be relevant to optically driven cold-atom systems. After introducing a broad class of models, we focus on particular realizations and show numerically that they exhibit topological order, as witnessed by topological ground-state degeneracies and the quantization of corresponding invariants. These results demonstrate that the correlations responsible for fractional quantum Hall states in lattices can arise in models involving terms other than density-density interactions.This work was supported in part by Engineering and Physical Sciences Research Council Grant No. EP/G049394/1, the Helmholtz Virtual Institute “New States of Matter and Their Excitations” and the EPSRC NetworkPlus on “Emergence and Physics far from Equilibrium”. S.K. acknowledges financial support by the ICAM Branch Contributions. The authors are grateful to M. Bukov, C. Chamon, N. R. Cooper, M. Daghofer, A. G. Grushin, C. Mudry, T. Neupert, and J. K. Pachos for stimulating discussions.This is the author accepted manuscript. The final version is available from the American Physical Society via http://dx.doi.org/10.1103/PhysRevB.91.15513

Free coherent spinons in quantum square ice

We investigate the quantum dynamics of monopole-like excitations in quantum square ice, as captured by the strongly anisotropic spin-1/2 XXZ model on the checkerboard lattice. We obtain exact results for excitation dynamics in both analytically solvable effective models and a fully interacting model of quantum square ice on finite clusters. We find that the dispersive lower bound of the dynamic response of freely propagating spinons is recovered in the dynamic structure factor of the interacting system, yielding a marked fingerprint of coherent spinon dispersion. Our results provide unbiased evidence for the formation of coherent quasiparticles propagating freely in the correlated "vacuum" of quantum square ice

Toric-boson model: Toward a topological quantum memory at finite temperature

We discuss the existence of stable topological quantum memory at finite temperature. At stake here is the fundamental question of whether it is, in principle, possible to store quantum information for macroscopic times without the intervention from the external world, that is, without error correction. We study the toric code in two dimensions with an additional bosonic field that couples to the defects, in the presence of a generic environment at finite temperature: the toric-boson model. Although the coupling constants for the bare model are not finite in the thermodynamic limit, the model has a finite spectrum. We show that in the topological phase, there is a finite temperature below which open strings are confined and therefore the lifetime of the memory can be made arbitrarily (polynomially) long in system size. The interaction with the bosonic field yields a long-range attractive force between the end points of open strings but leaves closed strings and topological order intact

D-wave superconductivity in boson+fermion dimer models

We present a slave-particle mean-field study of the mixed boson+fermion quantum dimer model introduced by Punk, Allais, and Sachdev [PNAS 112, 9552(2015)] to describe the physics of the pseudogap phase in cuprate superconductors. Our analysis naturally leads to four charge e fermion pockets whose total area is equal to the hole doping p, for a range of parameters consistent with the t-J model for high temperature superconductivity. Here we find that the dimers are unstable to d-wave superconductivity at low temperatures. The region of the phase diagram with d-wave rather than s-wave superconductivity matches well with the appearance of the four fermion pockets. In the superconducting regime, the dispersion contains eight Dirac cones along the diagonals of the Brillouin zone

Semiclassical approach to quantum spin ice

We propose a semi-classical description of the low-energy properties of quantum spin ice in the strong Ising limit. Within the framework of a semiclassical, perturbative Villain expansion, that can be truncated at arbitrary order, we give an analytic and quantitative treatment of the deconfining phase. We find that photon-photon interactions significantly renormalise the speed of light and split the two transverse photon polarisations at intermediate wavevectors. We calculate the photon velocity and the ground state energy to first and second order in perturbation theory, respectively. The former is in good agreement with recent numerical simulations