Non-Hermitian effects of the intrinsic signs in topologically ordered wavefunctions

Abstract

Negative signs in many-body wavefunctions play an important role in quantum mechanics because interference relies on cancellation between amplitudes of opposite signs. The ground-state wavefunction of double semion model contains negative signs that cannot be removed by any local transformation. Here we study the quantum effects of these intrinsic negative signs. By proposing a generic double semion wavefunction in tensor network representation, we show that its norm can be mapped to the partition function of a triangular lattice Ashkin-Teller model with imaginary interactions. We use numerical tensor-network methods to solve this non-Hermitian model with parity-time symmetry and determine a global phase diagram. In particular, we find a dense loop phase described by non-unitary conformal field theory and a parity-time-symmetry breaking phase characterized by the zeros of the partition function. Therefore, our work establishes a connection between the intrinsic signs in the topological wavefunction and non-unitary phases in the parity-time-symmetric non-Hermitian statistical model.

Galois conjugates of String-net Model

“…, {k/2}, where {a} means the integer part of number a. For example, Fibonacci model is in fact the subset of integer spin of su(2) 3 model, where we set g = 1 and deformation parameter q = e 2πi 5 . If we set g = 2, q = e 4πi 5 , what we actually get is Yang-Lee model, the non-unitarity comes from the possible negative sign of the function…”

“…The input data is that contained in a unitary fusion category -the unitary condition ensures that the Hamiltonian of the model is Hermitian. It is thus a curious question whether there are new topological orders if we relax the unitary condition [3][4][5]. Clearly, this is more than pure academic curiosity, since the existence of non-Hermitian topological orders would open the possibility to designing new classes of open systems to realize fault tolerant quantum computations.…”

Correlation effects on non-Hermitian point-gap topology in zero dimension: reduction of topological classification

“…Along with the above crucial progress in the noninteracting case, it turned out that correlation effects enrich topological phenomena as is the case of Hermitian sysetms [63][64][65][66][67][68][69][70][71][72][73] . For instance, it was reported that correlations induce topological ordered states such as fractional quantum Hall states 63,66 and spin liquid states 64,65,67 . In addition, a previous work addressed classification of symmetry-protected topological phases with the nontrivial line-gap topology which have Hermitian counter parts 74 .…”

Characterization of topological phase transitions from a non-Abelian topological state and its Galois conjugate through condensation and confinement order parameters

“…Here, the topological order is accompanied by the presence of certain group or Matrix Product Operator (MPO) symmetries in the entanglement degrees of freedom of the tensor, which can be used to parametrize the ground space manifold and anyonic excitations alike [7][8][9]. The description of topologically ordered systems as PEPS based on entanglement symmetries suggests a natural way to construct and study topological phase transitions within PEPS, by applying deformations to the physical degrees of freedom which drive the system to a different phase (such as a trivial product state) [10][11][12][13][14][15][16][17]. In this language, the entanglement symmetry in the tensor is preserved throughout the path, but at some point, it no longer manifests itself in topological order.…”