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Lukasz Fidkowski

Publications and source records attributed to Lukasz Fidkowski.

50 records · Page 3Linked to original sources
arXiv2012

Magnetic and Superconducting Ordering at LaAlO3/SrTiO3 Interfaces

We formulate a model for magnetic and superconducting ordering at LaAlO3/SrTiO3 interfaces containing both localized magnetic moments and itinerant electrons. Though these both originate in Ti 3d orbitals, the former may be due to electrons more tightly-bound to the interface while the latter are extended over several layers. Only the latter contribute significantly to metallic conduction and superconductivity. In our model, the interplay between the two types of electrons, which is argued to be ferromagnetic, combined with strong spin-orbit coupling of the itinerant electrons, leads to magnetic ordering. Furthermore, we propose a model for interfacial superconductivity, consisting of random superconducting grains in the bulk STO driven, via coupling to the interface conduction band, towards long-ranged or quasi-long-ranged order. Most interestingly, the magnetic order and strong spin orbit coupling can lead in this manner to unconventional interfacial superconductivity, yielding a possible realization of Majorana physics.

cond-mat.str-el↗
arXiv2011

Majorana Zero Modes in 1D Quantum Wires Without Long-Ranged Superconducting Order

We show that long-ranged superconducting order is not necessary to guarantee the existence of Majorana fermion zero modes at the ends of a quantum wire. We formulate a concrete model which applies, for instance, to a semiconducting quantum wire with strong spin-orbit coupling and Zeeman splitting coupled to a wire with algebraically-decaying superconducting fluctuations. We solve this model by bosonization and show that it supports Majorana fermion zero modes. We argue that a large class of models will also show the same phenomenon. We discuss the implications for experiments on spin-orbit coupled nanowires coated with superconducting film and for LaAlO3/SrTiO3 interfaces.

cond-mat.str-el↗
arXiv2011

Edge modes in band topological insulators

We characterize gapless edge modes in translation invariant topological insulators. We show that the edge mode spectrum is a continuous deformation of the spectrum of a certain gluing function defining the occupied state bundle over the Brillouin zone (BZ). Topologically non-trivial gluing functions, corresponding to non-trivial bundles, then yield edge modes exhibiting spectral flow. We illustrate our results for the case of chiral edge states in two dimensional Chern insulators, as well as helical edges in quantum spin Hall states.

cond-mat.str-el↗
arXiv2010

Topological phases of fermions in one dimension

In this paper we show how the classification of topological phases in insulators and superconductors is changed by interactions, in the case of 1D systems. We focus on the TR-invariant Majorana chain (BDI symmetry class). While the band classification yields an integer topological index $k$, it is known that phases characterized by values of $k$ in the same equivalence class modulo 8 can be adiabatically transformed one to another by adding suitable interaction terms. Here we show that the eight equivalence classes are distinct and exhaustive, and provide a physical interpretation for the interacting invariant modulo 8. The different phases realize different Altland-Zirnbauer classes of the reduced density matrix for an entanglement bipartition into two half-chains. We generalize these results to the classification of all one dimensional gapped phases of fermionic systems with possible anti-unitary symmetries, utilizing the algebraic framework of central extensions. We use matrix product state methods to prove our results.

cond-mat.str-el↗
arXiv2010

Entanglement spectrum of topological insulators and superconductors

We study two a priori unrelated constructions: the spectrum of edge modes in a band topological insulator or superconductor with a physical edge, and the ground state entanglement spectrum in an extended system where an edge is simulated by an entanglement bipartition. We prove an exact relation between the ground state entanglement spectrum of such a system and the spectrum edge modes of the corresponding spectrally flattened Hamiltonian. In particular, we show that degeneracies of the entanglement spectrum correspond to gapless edge modes.

cond-mat.str-el↗
arXiv2009

The effects of interactions on the topological classification of free fermion systems

We describe in detail a counterexample to the topological classification of free fermion systems. We deal with a one dimensional chain of Majorana fermions with an unusual T symmetry. The topological invariant for the free fermion classification is an integer, but with the introduction of interactions it becomes well defined only modulo 8. We illustrate this in the microscopic model of the Majorana chain by constructing an explicit path between two distinct free phases whose topological invariants are equal modulo 8, along which the system remains gapped. The path goes through a strongly interacting region. We also find the field theory interpretation of this phenomenon. There is a second order phase transition between the two phases in the free theory which can be avoided by going through the strongly interacting region. We show that this transition is in the 2D Ising universality class, where a first order phase transition line, terminating at a second order transition, can be avoided by going through the analogue of a high temperature paramagnetic phase. In fact, we construct the full phase diagram of the system as a function of the thermal operator (i.e. the mass term that tunes between the two phases in the free theory) and two quartic operators, obtaining a first order Peierls transition region, a second order transition region, and a region with no transition.

cond-mat.str-el↗
arXiv2008

Permutation Symmetric Critical Phases in Disordered Non-Abelian Anyonic Chains

Topological phases supporting non-abelian anyonic excitations have been proposed as candidates for topological quantum computation. In this paper, we study disordered non-abelian anyonic chains based on the quantum groups $SU(2)_k$, a hierarchy that includes the $ν=5/2$ FQH state and the proposed $ν=12/5$ Fibonacci state, among others. We find that for odd $k$ these anyonic chains realize infinite randomness critical {\it phases} in the same universality class as the $S_k$ permutation symmetric multi-critical points of Damle and Huse (Phys. Rev. Lett. 89, 277203 (2002)). Indeed, we show that the pertinent subspace of these anyonic chains actually sits inside the ${\mathbb Z}_k \subset S_k$ symmetric sector of the Damle-Huse model, and this ${\mathbb Z}_k$ symmetry stabilizes the phase.

cond-mat.str-el↗
arXiv2008

Infinite Randomness Phases and Entanglement Entropy of the Disordered Golden Chain

Topological insulators supporting non-abelian anyonic excitations are at the center of attention as candidates for topological quantum computation. In this paper, we analyze the ground-state properties of disordered non-abelian anyonic chains. The resemblance of fusion rules of non-abelian anyons and real space decimation strongly suggests that disordered chains of such anyons generically exhibit infinite-randomness phases. Concentrating on the disordered golden chain model with nearest-neighbor coupling, we show that Fibonacci anyons with the fusion rule $τ\otimesτ={\bf 1}\oplus τ$ exhibit two infinite-randomness phases: a random-singlet phase when all bonds prefer the trivial fusion channel, and a mixed phase which occurs whenever a finite density of bonds prefers the $τ$ fusion channel. Real space RG analysis shows that the random-singlet fixed point is unstable to the mixed fixed point. By analyzing the entanglement entropy of the mixed phase, we find its effective central charge, and find that it increases along the RG flow from the random singlet point, thus ruling out a c-theorem for the effective central charge.

cond-mat.str-el↗
arXiv2007

Double Point Contact in the k=3 Read-Rezayi State

We compute the dependence of the tunneling current in a double point contact in the k=3 Read-Rezayi state (which is conjectured to describe an incompressible quantum hall fluid at filling fraction nu=12/5) on voltage, separation between the two contacts, and temperature. Using the tunneling hamiltonian of cond-mat/0607431, we show that the effect of quasiholes in the bulk region between the two contacts is simply an overall constant multiplying the interference term. This is the same effect as found for the differential conductivity in cond-mat/0601242; the difference is that we do an actual edge theory calculation and compute the full current-voltage curve at weak tunneling.

cond-mat.mes-hall↗
arXiv2007

A new equivalence between fused RSOS and loop models

We consider the topological theories of cond-mat/0404617 and cond-mat/0610583 and study ground state amplitudes of string net configurations which consist of large chunks $G$ of (trivalent) regular lattice. We evaluate these amplitudes in two different ways: first we use the Turaev-Viro prescription to write the amplitude as a sum over labelings of the faces of $G$, and second we use the local rules that constrain the amplitude (the $F$-matrix) to resolve subgraphs in creative ways. In the case of the Doubled Fibonacci theory this second way allows us to produce loop models. In particular, we show that the hard hexagon model is equivalent to an anisotropic loop model. Many other interesting equivalences can presumably be obtained.

cond-mat.stat-mech↗
arXiv2006

From String Nets to Nonabelions

We discuss Hilbert spaces spanned by the set of string nets, i.e. trivalent graphs, on a lattice. We suggest some routes by which such a Hilbert space could be the low-energy subspace of a model of quantum spins on a lattice with short-ranged interactions. We then explain conditions which a Hamiltonian acting on this string net Hilbert space must satisfy in order for its ground state and low-lying quasiparticle excitations to be in the DFib topological phase. Using the string net wavefunction, we describe the properties of this phase. Our discussion is informed by mappings of string net wavefunctions to the chromatic polynomial and the Potts model.

cond-mat.str-el↗
arXiv2004

D-Brane Instability as a Large N Phase Transition

In AdS/CFT analyticity suggests that certain singular behaviors expected at large 't Hooft coupling should continue smoothly to weak 't Hooft coupling where the gauge theory is tractable. This may provide a window into stringy singularity resolution and is a promising technique for studying the signature of the black hole singularity discussed in hep-th/0306170. We comment briefly on its status. Our main goal, though, is to study a simple example of this technique. Gross and Ooguri (hep-th/9805129) have pointed out that the D-brane minimal surface spanning a pair of 't Hooft loops undergoes a phase transition as the distance between the loops is varied. We find the analog of this behavior in the weakly coupled Super Yang Mills theory by computing 't Hooft loop expectation values there.

hep-th↗
arXiv2003

The Black Hole Singularity in AdS/CFT

We explore physics behind the horizon in eternal AdS Schwarzschild black holes. In dimension d >3, where the curvature grows large near the singularity, we find distinct but subtle signals of this singularity in the boundary CFT correlators. Building on previous work, we study correlation functions of operators on the two disjoint asymptotic boundaries of the spacetime by investigating the spacelike geodesics that join the boundaries. These dominate the correlators for large mass bulk fields. We show that the Penrose diagram for d>3 is not square. As a result, the real geodesic connecting the two boundary points becomes almost null and bounces off the singularity at a finite boundary time t_c \neq 0. If this geodesic were to dominate the correlator there would be a "light cone" singularity at t_c. However, general properties of the boundary theory rule this out. In fact, we argue that the correlator is actually dominated by a complexified geodesic, whose properties yield the large mass quasinormal mode frequencies previously found for this black hole. We find a branch cut in the correlator at small time (in the limit of large mass), arising from coincidence of three geodesics. The t_c singularity, a signal of the black hole singularity, occurs on a secondary sheet of the analytically continued correlator. Its properties are computationally accessible. The t_c singularity persists to all orders in the 1/m expansion, for finite α', and to all orders in g_s. Certain leading nonperturbative effects can also be studied. The behavior of these boundary theory quantities near t_c gives, in principle, significant information about stringy and quantum behavior in the vicinity of the black hole singularity.

hep-th↗