A quantum phase transition (QPT) in Hermitian systems is independent of the boundary condition in the thermodynamic limit. However, it may happen for a non-Hermitian system, that the QPT strongly depends on the boundary condition. We investigate the many-body ground-state property of a one-dimensional tight-binding ring with an embedded single asymmetrical dimer based on exact solutions. We employ a semilocalization state to describe a quantum phase that is a crossover from extended to localized state. The peculiar feature is that the decay length is of the order of the system size rather than fixed as a usual localized state. In addition, the spectral statistics is nonanalytic as asymmetrical hopping strengths vary, resulting a sudden charge of the ground state. The distinguishing feature of such a QPT is that the density of the ground-state energy varies smoothly due to unbroken symmetry. However, there are other observables, such as the ground-state center of mass and average current, which exhibit the behavior of second-order QPT. This behavior stems from time-reversal symmetry breaking of a macroscopic number of single-particle eigenstates.
Quantum phase transitions are sudden changes in the ground-state wavefunction of a many-body system that can occur as a control parameter such as a concentration or a field strength is varied. They are driven purely by the competition between quantum fluctuations and mutual interactions among constituents of the system, not by thermal fluctuations; hence they can occur even at zero temperature. Examples of quantum phase transitions in many-body physics may be found in systems ranging from high-temperature superconductors to topological insulators. A quantum phase transition usually can be characterized by nonanalyticity/discontinuity in certain order parameters or divergence of the ground state energy eigenvalue and/or its derivatives with respect to certain physical quantities. Here in a circular one-dimensional spin model with Heisenberg XY interaction and no magnetic field, we observe critical phenomena for the
n0=1/N→0 Mott insulator caused by a qualitative change of the boundary condition. We demonstrate in the vicinity of the transition point a sudden change in ground-state properties accompanied by an avoided level-crossing between the ground and the first excited states. Notably, our result links conventional quantum phase transitions to microscopic boundary conditions, with significant implications for quantum information, quantum control, and quantum computing.
Recent studies on disorder-induced many-body localization (MBL) in non-Hermitian quantum systems have attracted great interest. However, the non-Hermitian disorder-free MBL still needs to be clarified. We consider a one-dimensional interacting Stark model with nonreciprocal hoppings having time-reversal symmetry, the properties of which are boundary dependent. Under periodic boundary conditions (PBCs), such a model exhibits three types of phase transitions: the real-complex transition of eigenenergies, the topological phase transition, and the non-Hermitian Stark MBL transition. The real-complex and topological phase transitions occur at the same point in the thermodynamic limit but do not coincide with the non-Hermitian Stark MBL transition, which is quite different from the non-Hermitian disordered cases. By the level statistics, the system transitions from the Ginibre ensemble (GE) to the Gaussian orthogonal ensemble (GOE) to the Possion ensemble with the increase of the linear tilt potential's strength. The real-complex transition of the eigenvalues is accompanied by the GE-to-GOE transition in the ergodic regime. Moreover, the second transition of the level statistics corresponds to the occurrence of non-Hermitian Stark MBL. We demonstrate that the non-Hermitian Stark MBL is robust and shares many similarities with disorder-induced MBL, which several existing characteristic quantities of the spectral statistics and eigenstate properties can confirm. The dynamical evolutions of the entanglement entropy and the density imbalance can distinguish the real-complex and Stark MBL transitions. Finally, we find that our system under open boundary conditions lacks a real-complex transition, and the transition of non-Hermitian Stark MBL is the same as that under PBCs.
A quantum phase transition (QPT), including both topological and symmetry breaking types, is usually induced by the change of global parameters, such as external fields or global coupling constants. In this work, we demonstrate the existence of QPT induced by the real-space topology of the system. We investigate the groundstate properties of the tight-binding model on a honeycomb lattice with the torus geometry based on exact results. It is shown that the ground state experiences a second-order QPT, exhibiting the scaling behavior, when the torus switches to a tube, which reveals the connection between quantum phase and the real-space topology of the system.
The non-Hermitian systems exhibit extreme sensitivity to the boundary conditions. The change in the eigenspectrum with tuning boundary parameter is intimately connected to the non-Hermitian skin effect. The single-particle systems are affected by the boundary perturbations; however, the interplay of a random disorder potential and nonreciprocal hopping under boundary perturbations of an interacting many-body system is not yet clear. In this work, we examine the boundary sensitivity of a non-Hermitian interacting fermionic system in the presence of a random disorder potential. A nonzero boundary parameter results in real-complex spectral transitions with nonreciprocal (or unidirectional) hopping at weak disorder, while the many-body localization at strong disorder washes away real-complex transitions leading to dynamical stability and real eigenvalue spectrum. We show that the boundary-driven real-complex spectral transitions of the non-Hermitian chain are accompanied by the corresponding changes in the level statistics and nearest level-spacing distributions. The intriguing features of nonreciprocity and boundary sensitivity are further revealed using the averaged inverse participation ratios. Finally, we find distinct behavior in the quench dynamics of local particle density, population imbalance, and entanglement entropy of charge-density-wave ordered state that corroborate the real-complex and localization transitions. Our results provide a route to understanding disordered many-body systems under a generalized boundary.
We study the Hatano-Nelson model, i.e., a one-dimensional non-Hermitian chain of spinless fermions with nearest-neighbor nonreciprocal hopping, in the presence of repulsive nearest-neighbor interactions. At half filling, we find two
PT transitions, as the interaction strength increases. The first transition is marked by an exceptional point between the first and the second excited state in a finite-size system and is a first-order symmetry-breaking transition into a charge-density wave regime. Persistent currents characteristic of the Hatano-Nelson model abruptly vanish at the transition. The second transition happens at a critical interaction strength that scales with the system size and can thus only be observed in finite-size systems. It is characterized by a collapse of all energy eigenvalues onto the real axis. We further show that in a strong interaction regime, but away from half filling, the many-body spectrum shows point gaps with nontrivial winding numbers, akin to the topological properties of the single-particle spectrum of the Hatano-Nelson chain, which indicates the skin effect of extensive many-body eigenstates under open boundary conditions. Our results can be applied to other models such as the non-Hermitian Su-Schrieffer-Heeger-type model and contribute to an understanding of fermionic many-body systems with non-Hermitian Hamiltonians.
Non-Hermitian spin systems have attracted extensive interest due to their unconventional magnetic properties, rich entanglement resources, and unusual quantum criticality phenomena. In this paper, based on the exact solution of a one-dimensional non-Hermitian spin-1/2 XY model with rotation-time-reversal (
RT) symmetry [X. Z. Zhang et al., Phys. Rev. A 87, 012114 (2013)], we study the ground-state energy density, magnetization, correlation functions, quantum entanglement, and correlation in
RT-symmetric and
RT-broken phases as well as their characteristics at the exceptional point. We find that the energy density rises faster with the non-Hermitian parameter $|\ensuremath{\gamma}|$ in the symmetric region than in the broken one and is elevated rapidly at the exceptional point, and the decay of magnetization has similar results. We analyze the effect of $\ensuremath{\gamma}$ on the system and find that the energy density decreases linearly with the external magnetic field
h for $\ensuremath{\gamma}>0,$ while it is bifurcated when $\ensuremath{\gamma}=0$. In addition, the behaviors of the energy density indicate that the phase transition caused by symmetry breaking is second order, which is further demonstrated by the magnetization, quantum entanglement, etc. The numerical results of the correlation functions surprisingly indicate that the
RT-broken phase has quasi-long-range order, which is quite different from the Hermitian XY model. Especially, the crossover behavior of the ground-state entanglement shows that it increases with $\ensuremath{\gamma}$ in the symmetric region, which is opposite to the case of the broken one, and its maximum always appears at the exceptional point. The above behaviors at the phase boundary are actually ascribed to the fierce competition between $\ensuremath{\gamma}$ and
h, which results in a rapid decline of magnetization and the appearance of the maximum of entanglement.