Parity-time (PT) non-Hermitian (NH) system has significant effects on observable in a great variety of physical phenomena in NH physics. However, the PT-symmetric NH quantum system at finite temperature (the so-called thermal PT system) has never bee
n addressed. In this letter, based on a controlled open quantum system coupling two separated environments, we proposed a design to realize a thermal PT system. After solving quantum master equation in the Gorini-KossakowskiSudarshan-Lindblad form, the unexpected, abnormal, universal properties of NH thermal states (the unique final states under time evolution) are explored, for example, the non-Boltzmann/Gibbs distribution, high-temperature non-thermalization effect, etc. To understand the anomalous behaviours in thermal PT system, we developed the quantum Liouvillian statistical theory-the generalization of usual quantum statistical theory to finite-temperature NH systems. With its help, we derived the analytical results of thermodynamic properties. In addition, we found that at exceptional point (EP) a continuous thermodynamic phase transition occurs, of which there exists zero temperature anomaly. This discovery will open a door to novel physics for NH systems at finite temperature.
We show that non-Hermitian biorthogonal many-body phase transitions can be characterized by the enhanced decay of Loschmidt echo. The quantum criticality is numerically investigated in a non-Hermitian transverse field Ising model by performing the fi
nite-size dynamical scaling of Loschmidt echo. We determine the equilibrium correlation length critical exponents that are consistent with previous results from the exact diagonalization. More importantly, we introduce a simple method to detect quantum phase transitions with the short-time average of rate function motivated by the critically enhanced decay behavior of Loschmidt echo. Our studies show how to detect equilibrium many-body phase transitions with biorthogonal Loschmidt echo that can be observed in future experiments via quantum dynamics after a quench.
We investigate the number-anomalous of the Majorana zero modes in the non-Hermitian Kitaev chain, whose hopping and superconductor paring strength are both imbalanced. We find that the combination of two imbalanced non-Hermitian terms can induce defe
ctive Majorana edge states, which means one of the two localized edge states will disappear due to the non-Hermitian suppression effect. As a result, the conventional bulk-boundary correspondence is broken down. Besides, the defective edge states are mapped to the ground states of non-Hermitian transverse field Ising model, and the global phase diagrams of ferromagnetic-antiferromagnetic crossover for ground states are given. Our work, for the first time, reveal the break of topological robustness for the Majorana zero modes, which predict more novel effects both in topological material and in non-Hermitian physics.
We develop the perturbation theory of the fidelity susceptibility in biorthogonal bases for arbitrary interacting non-Hermitian many-body systems with real eigenvalues. The quantum criticality in the non-Hermitian transverse field Ising chain is inve
stigated by the second derivative of ground-state energy and the ground-state fidelity susceptibility. We show that the system undergoes a second-order phase transition with the Ising universal class by numerically computing the critical points and the critical exponents from the finite-size scaling theory. Interestingly, our results indicate that the biorthogonal quantum phase transitions are described by the biorthogonal fidelity susceptibility instead of the conventional fidelity susceptibility.
The chiral QED$_3$--Gross-Neveu-Yukawa (QED$_3$-GNY) theory is a $2+1$-dimensional U(1) gauge theory with $N_f$ flavors of four-component Dirac fermions coupled to a scalar field. For $N_f=1$, the specific chiral Ising QED$_3$-GNY model has recently
been conjectured to be dual to the deconfined quantum critical point that describes Neel--valence-bond-solid transition of frustrated quantum magnets on square lattice. We study the universal critical behaviors of the chiral QED$_3$-GNY model in $d=4-epsilon$ dimensions for an arbitrary $N_f$ . We calculate the boson anomalous dimensions, inverse correlation length exponent, as well as the scaling dimensions of nonsinglet fermion bilinear in the chiral QED$_3$-GNY model. The Pad$acute{e}$ estimates for the exponents are obtained in the chiral Ising-, XY- and Heisenberg-QED$_3$-GNY universality class respectively. We also establish the general condition of the supersymmetric criticality for the ungauged QED$_3$-GNY model. For the conjectured duality between chiral QED$_3$-GNY critical point and deconfined quantum critical point, we find the inverse correlation length exponent has a lower boundary $ u^{-1}>0.75$, beyond which the Ising-QED$_3$-GNY--$mathbb{C}$P$^1$ duality may hold.
The fluctuations-driven continuous quantum criticality has sparked tremendous interest in condensed matter physics. It has been verified that the gapless fermions fluctuations can change the nature of phase transition at criticality. In this paper, w
e study the fermionic quantum criticality with enlarged Ising$times$Ising fluctuations in honeycomb lattice materials. The Gross-Neveu-Yukawa theory for the multicriticality between the semimetallic phase and two ordered phases that break Ising symmetry is investigated by employing perturbative renormalization group approach. We first determine the critical range in which the quantum fluctuations may render the phase transition continuous. We find that the Ising criticality is continuous only when the flavor numbers of four-component Dirac fermions $N_fgeq1/4$. Using the $epsilon$ expansion in four space-time dimensions, we then study the Ising$times$Ising multicriticality stemming from the symmetry-breaking electronic instabilities. We analyze the underlying fixed-point structure and compute the critical exponents for the Ising$times$Ising Gross-Neveu-Yukawa universality class. Further, the correlation scaling behavior for the fermion bilinear on the honeycomb lattice at the multicritical point are also briefly discussed.
The breakdown of the bulk-boundary correspondence in non-Hermitian (NH) topological systems is an open, controversial issue. In this paper, to resolve this issue, we ask the following question: Can a (global) topological invariant completely describe
the topological properties of a NH system as its Hermitian counterpart? Our answer is no. One cannot use a global topological invariant (including non-Bloch topological invariant) to accurately characterize the topological properties of the NH systems. Instead, there exist a new type of topological invariants that are absence in its Hermitian counterpart -- the state dependent topological invariants. With the help of the state-dependent topological invariants, we develop a new topological theory for NH topological system beyond the general knowledge for usual Hermitian systems and obtain an exact formulation of the bulk-boundary correspondence, including state-dependent phase diagram, state-dependent phase transition and anomalous transport properties (spontaneous topological current). Therefore, these results will help people to understand the exotic topological properties of various non-Hermitian systems.
Deconfined quantum critical point was proposed as a second-order quantum phase transition between two broken symmetry phases beyond the Landau-Ginzburg-Wilson paradigm. However, numerical studies cannot completely rule out a weakly first-order transi
tion because of strong violations of finite-size scaling. We demonstrate that the fidelity is a simple probe to study deconfined quantum critical point. We study the ground-state fidelity susceptibility close to the deconfined quantum critical point in a spin chain using the large-scale finite-size density matrix renormalization group method. We find that the finite-size scaling of the fidelity susceptibility obeys the conventional scaling behavior for continuous phase transitions, supporting the deconfined quantum phase transition is continuous. We numerically determine the deconfined quantum critical point and the associated correlation length critical exponent from the finite-size scaling theory of the fidelity susceptibility. Our results are consistent with recent results obtained directly from the matrix product states for infinite-size lattices using others observables. Our work provides a useful probe to study critical behaviors at deconfined quantum critical point from the concept of quantum information.
In view of the recent experimental facts in the iron-pnictides, we make a proposal that the itinerant electrons and local moments are simultaneously present in such multiband materials. We study a minimal model composed of coupled itinerant electrons
and local moments to illustrate how a consistent explanation of the experimental measurements can be obtained in the leading order approximation. In this mean-field approach, the spin-density-wave (SDW) order and superconducting pairing of the itinerant electrons are not directly driven by the Fermi surface nesting, but are mainly induced by their coupling to the local moments. The presence of the local moments as independent degrees of freedom naturally provides strong pairing strength for superconductivity and also explains the normal-state linear-temperature magnetic susceptibility above the SDW transition temperature. We show that this simple model is supported by various anomalous magnetic properties and isotope effect which are in quantitative agreement with experiments.
In this paper, we analyze the quantum phases of multiple component Bose-Hubbard model in optical superlattices, using a mean-field method, the decoupling approximation. We find that the phase diagrams exhibit complected patterns and regions with vari
ous Charge Density Wave (CDW) for both one- and two- component cases. We also analyze the effective spin dynamics for the two-component case in strong-coupling region at unit filling, and show the possible existence of a Spin Density Wave (SDW) order.
