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The quantum phase diagram and critical behavior of two-dimensional Dirac fermions coupled to two compatible order-parameter fields with $O(N_1)\oplus O(N_2)$ symmetry is investigated. Recent numerical studies of such systems have reported…
We demonstrate the occurrence of nodal non-Hermitian (NH) phases featuring exceptional degeneracies in chiral-symmetric disordered quantum wires, where NH physics naturally arises from the self-energy in a disorder-averaged Green's function…
By implementing a charge pumping scheme for one-dimensional aperiodic chains, we confirm the existence of topological phases in these systems whenever their finite-size realizations admit inversion symmetry. These phases are usually…
We investigate the effects of quenched randomness on topological quantum phase transitions in strongly interacting two-dimensional systems. We focus first on transitions driven by the condensation of a subset of fractionalized…
We show that chains of interacting Fibonacci anyons can support a wide variety of collective ground states ranging from extended critical, gapless phases to gapped phases with ground-state degeneracy and quasiparticle excitations. In…
In recent years, fermionic topological phases of quantum matter has attracted a lot of attention. In a pioneer work by Gu, Wang and Wen, the concept of equivalence classes of fermionic local unitary(FLU) transformations was proposed to…
We examine the effective field theory of the Bethe ansatz integrable Heisenberg antiferromagnetic spin chains. It shows that the quantum critical theories for the integer spin-S chains should be characterized by the SO(3)level-S…
We show that different classes of topological order can be distinguished by the dynamical symmetry algebra of edge excitations. Fundamental topological order is realized when this algebra is the largest possible, the algebra of quantum…
The non-abelian topological phase with Fibonacci anyons minimally supports universal quantum computation. In order to investigate the possible phase transitions out of the Fibonacci topological phase, we propose a generic quantum-net…
A topological phase can undergo a phase transition driven by anyon condensation. A potential obstruction to such a mechanism could arise if there exists a symmetry between anyons that have non-trivial mutual statistics. Here we consider…
The quantum phase transition between two clean, non interacting topologically distinct gapped states in three dimensions is governed by a massless Dirac fermion fixed point, irrespective of the underlying symmetry class, and this…
We discuss a certain class of two-dimensional quantum systems which exhibit conventional order and topological order, as well as two-dimensional quantum critical points separating these phases. All of the ground-state equal-time correlators…
We study the quantum multicritical point in a (2+1)-dimensional Dirac system between the semimetallic phase and two ordered phases that are characterized by anticommuting mass terms with $O(N_1)$ and $O(N_2)$ symmetry, respectively. Using…
There are many interesting parallels between systems of interacting non-Abelian anyons and quantum magnetism, occuring in ordinary SU(2) quantum magnets. Here we consider theories of so-called su(2)_k anyons, well-known deformations of…
We find a series of possible continuous quantum phase transitions between fractional quantum Hall (FQH) states at the same filling fraction in two-component quantum Hall systems. These can be driven by tuning the interlayer tunneling and/or…
We study symmetry breaking quantum phase transitions in topological insulators and superconductors where the single electron gap remains open in the bulk. Specifically, we consider spontaneous breaking of the symmetry that protects the…
The hallmark of a 2 dimensional topologically ordered phase is the existence of deconfined `anyon' excitations that have exotic braiding and exchange statistics, different from those of ordinary bosons or fermions. As opposed to…
We propose a family of Abelian quantum Hall states termed the non-diagonal states, which arise at filling factors $\nu=p/2q$ for bosonic systems and $\nu=p/(p+2q)$ for fermionic systems, with $p$ and $q$ being two coprime integers.…
Non-Abelian topological orders offer an intriguing path towards fault-tolerant quantum computation, where information can be encoded and manipulated in a topologically protected manner immune to arbitrary local noises and perturbations.…
We report an extremely rich ground state phase diagram of two spin-1 Haldane chains frustrated with a three-site exchange and coupled by the antiferromagnetic Heisenberg interaction on a zig-zag ladder. A particular feature of the phase…