Gapped quantum liquids and topological order, stochastic local transformations and emergence of unitarity

In this work we present some new understanding of topological order, including three main aspects: (1) It was believed that classifying topological orders corresponds to classifying gapped quantum states. We show that such a statement is not precise. We introduce the concept of \emph{gapped quantum liquid} as a special kind of gapped quantum states that can "dissolve" any product states on additional sites. Topologically ordered states actually correspond to gapped quantum liquids with stable ground-state degeneracy. Symmetry-breaking states for on-site symmetry are also gapped quantum liquids, but with unstable ground-state degeneracy. (2) We point out that the universality classes of generalized local unitary (gLU) transformations (without any symmetry) contain both topologically ordered states and symmetry-breaking states. This allows us to use a gLU invariant -- topological entanglement entropy -- to probe the symmetry-breaking properties hidden in the exact ground state of a finite system, which does not break any symmetry. This method can probe symmetry- breaking orders even without knowing the symmetry and the associated order parameters. (3) The universality classes of topological orders and symmetry-breaking orders can be distinguished by \emph{stochastic local (SL) transformations} (i.e.\ \emph{local invertible transformations}): small SL transformations can convert the symmetry-breaking classes to the trivial class of product states with finite probability of success, while the topological-order classes are stable against any small SL transformations, demonstrating a phenomenon of emergence of unitarity. This allows us to give a new definition of long-range entanglement based on SL transformations, under which only topologically ordered states are long-range entangled.Comment: Revised version. Figures and references adde

In-plane dissipation as a possible synchronization mechanism for terahertz radiation from intrinsic Josephson junctions of layered superconductors

Strong terahertz radiation from mesa structure of $\rm{Bi_2Sr_2CaCu_2O_{8+\delta}}$ single crystal has been observed recently, where the mesa intrinsically forms a cavity. For a thick mesa of large number of junctions, there are many cavity modes with different wave vectors along the c-axis corresponding to almost degenerate bias voltages. The mechanism responsible for exciting the uniform mode which radiates coherent terahertz waves in experiments is unknown. In this work, we show that the in-plane dissipation selects the uniform mode. For perturbations with non-zero wave numbers along the c-axis, the in-plane dissipations are significantly enhanced, which prevent the excitation of corresponding cavity modes. Our analytical results are confirmed by numerical simulations.Comment: 7 pages, 5 figure

Holographic Van der Waals phase transition for a hairy black hole

The Van der Waals(VdW) phase transition in a hairy black hole is investigated by analogizing its charge, temperature, and entropy as the temperature, pressure, and volume in the fluid respectively. The two point correlation function(TCF), which is dual to the geodesic length, is employed to probe this phase transition. We find the phase structure in the temperature$-$geodesic length plane resembles as that in the temperature$-$thermal entropy plane besides the scale of the horizontal coordinate. In addition, we find the equal area law(EAL) for the first order phase transition and critical exponent of the heat capacity for the second order phase transition in the temperature$-$geodesic length plane are consistent with that in temperature$-$thermal entropy plane, which implies that the TCF is a good probe to probe the phase structure of the back hole.Comment: Accepted by Advances in High Energy Physics(The special issue: Applications of the Holographic Duality to Strongly Coupled Quantum Systems

Van der Waals phase transition in the framework of holography

Phase structure of the quintessence Reissner-Nordstr\"{o}m-AdS black hole is probed with the nonlocal observables such as holographic entanglement entropy and two point correlation function. Our result shows that, as the case of the thermal entropy, both the observables exhibit the similar Van der Waals-like phase transition. To reinforce the conclusion, we further check the equal area law for the first order phase transition and critical exponent of the heat capacity for the second order phase transition. We also discuss the effect of the state parameter on the phase structure of the nonlocal observables.Comment: 16 pages, 6 figures. arXiv admin note: text overlap with arXiv:1511.0038