Entanglement provides characterizing features of true topological order in two-dimensional systems. We show how entanglement of disconnected partitions defines topological invariants for one-dimensional topological superconductors. These order parameters quantitatively capture the entanglement that is possible to distill from the ground-state manifold and are thus quantized to 0 or $log2$ . Their robust quantization property is inferred from the underlying lattice gauge theory description of topological superconductors and is corroborated via exact solutions and numerical simulations. Transitions between topologically trivial and nontrivial phases are accompanied by scaling behavior, a hallmark of genuine order parameters, captured by entanglement critical exponents. These order parameters are experimentally measurable utilizing state-of-the-art techniques.Entanglement provides characterizing features of true topological order in two-dimensional systems. We show how entanglement of disconnected partitions defines topological invariants for one-dimensional topological superconductors. These order parameters quantitatively capture the entanglement that is possible to distill from the ground-state manifold and are thus quantized to 0 or $log2$. Their robust quantization property is inferred from the underlying lattice gauge theory description of topological superconductors and is corroborated via exact solutions and numerical simulations. Transitions between topologically trivial and nontrivial phases are accompanied by scaling behavior, a hallmark of genuine order parameters, captured by entanglement critical exponents. These order parameters are experimentally measurable utilizing state-of-the-art techniques.

arXiv:1909.04035Physical review. B./Physical review. BFeb 24, 202056 citations

Exact solution for the superconducting transition in one dimension

S. Marĉelja

Physics Letters AJun 1, 19714 citations

Estimate of the critical region for the Kosterlitz-Thouless transition

Petter Minnhagen, Peter Olsson

The width of the critical region for the Kosterlitz-Thouless transition is estimated and found to be extremely narrow. The estimate is based on a numerical solution of a set of renormalization equations for the two-dimensional Coulomb gas. It is concluded that the Kosterlitz-Thouless critical behavior cannot be observed in the resistance data for quasi-two-dimensional superconductors. The implications for the quasi-two-dimensionality of high- ${\mathit{T}}_{\mathit{c}}$ superconductors are discussed.The width of the critical region for the Kosterlitz-Thouless transition is estimated and found to be extremely narrow. The estimate is based on a numerical solution of a set of renormalization equations for the two-dimensional Coulomb gas. It is concluded that the Kosterlitz-Thouless critical behavior cannot be observed in the resistance data for quasi-two-dimensional superconductors. The implications for the quasi-two-dimensionality of high-${\mathit{T}}_{\mathit{c}}$ superconductors are discussed.

Physical review. B, Condensed matterMay 1, 199216 citations

Studies on two topics in theoretical physics: Entanglement entropy and holographic superconductors

Shiying Dong

This thesis contains two parts. The _rst part consists of the _rst two chapters, studying the entanglement entropy. The second part consists of the third chapter, dealing with holographic superconductors. In chapter one we calculate the topological entanglement entropy of Chern-Simons theories in 2+1 dimensions. We employ a procedure of surgery to do the calculation, and _nd the general formula for the entanglement entropy for any state on any smooth surface. The key component of the result is the so-called S matrices of the WZW models associated with our Chern-Simons theories. We apply our results to the quantum Hall uids that are described by various kinds of Chern-Simons theories and calculate their S matrix elements. In chapter two we study the entanglement entropy for the nontrivial primary states of a two dimensional CFT, the free boson. We use several tricks to help us go through the calculation and get the exact results for several primary states. In chapter three we discuss a model of holographic superconductors. It is a (3+1)- dimensional Abelian-Higgs model of gravity with negative cosmological constant. We study the static, spherically symmetric solutions of this model numerically. These are hairy black holes.The nonzero hair corresponds to the nonzero expectation value of some composite operator in the dual _eld theory. We _nd the second order phase transition at certain critical temperature Tc and a mean _eld critical exponent of 0.5. The low temperature behavior of this model does not conform to that of a superconductor however. We also study the static, axially symmetric solutions (vortex solutions), especially their thermodynamical properties. A numerical algorithm to _nd such solutions is setup, with all the key steps solved.This thesis contains two parts. The _rst part consists of the _rst two chapters, studying the entanglement entropy. The second part consists of the third chapter, dealing with holographic superconductors. In chapter one we calculate the topological entanglement entropy of Chern-Simons theories in 2+1 dimensions. We employ a procedure of surgery to do the calculation, and _nd the general formula for the entanglement entropy for any state on any smooth surface. The key component of the result is the so-called S matrices of the WZW models associated with our Chern-Simons theories. We apply our results to the quantum Hall uids that are described by various kinds of Chern-Simons theories and calculate their S matrix elements. In chapter two we study the entanglement entropy for the nontrivial primary states of a two dimensional CFT, the free boson. We use several tricks to help us go through the calculation and get the exact results for several primary states. In chapter three we discuss a model of holographic superconductors. It is a (3+1)- dimensional Abelian-Higgs model of gravity with negative cosmological constant. We study the static, spherically symmetric solutions of this model numerically. These are hairy black holes.The nonzero hair corresponds to the nonzero expectation value of some composite operator in the dual _eld theory. We _nd the second order phase transition at certain critical temperature Tc and a mean _eld critical exponent of 0.5. The low temperature behavior of this model does not conform to that of a superconductor however. We also study the static, axially symmetric solutions (vortex solutions), especially their thermodynamical properties. A numerical algorithm to _nd such solutions is setup, with all the key steps solved.

Aug 31, 20100 citations

Theory of critical phenomena in superconductors : quantum field theoretical approach

一高山

Jan 1, 19720 citations

log2

. Their robust quantization property is inferred from the underlying lattice gauge theory description of topological superconductors and is corroborated via exact solutions and numerical simulations. Transitions between topologically trivial and nontrivial phases are accompanied by scaling behavior, a hallmark of genuine order parameters, captured by entanglement critical exponents. These order parameters are experimentally measurable utilizing state-of-the-art techniques.

{\mathit{T}}_{\mathit{c}}

superconductors are discussed.