Abstract Non-Hermitian (NH) quantum system recently have attracted a lots of attentions theoretically and experimentally. However, the results based on the single-particle picture may not apply to understand the property of NH many-body system. How the property of quantum many-body system especially the phase transition will be affected by the non-Hermiticity remains unclear. Here we study NH quantum contact process (QCP) model, whose effective Hamiltonian is derived from Lindbladian master equation. We show that there is a continuous phase transition induced by the non-Hermiticity in QCP. We also determine the critical exponents β of order parameter, γ of susceptibility and study the correlation and entanglement near phase transition point. We observe that the order parameter and susceptibility display infinitely singularity even for finite size system, since non-Hermiticity endow many-body system with different singular behavior from classical phase transition. Moreover our results show that the phase transition have no counterpart in Hermitian case and belongs to completely different universality class.
Abstract Non-Hermitian (NH) quantum system recently have attracted a lots of attentions theoretically and experimentally. However, the results based on the single-particle picture may not apply to understand the property of NH many-body system. How the property of quantum many-body system especially the phase transition will be affected by the non-Hermiticity remains unclear. Here we study NH quantum contact process (QCP) model, whose effective Hamiltonian is derived from Lindbladian master equation. We show that there is a continuous phase transition induced by the non-Hermiticity in QCP. We also determine the critical exponents β of order parameter, γ of susceptibility and study the correlation and entanglement near phase transition point. We observe that the order parameter and susceptibility display infinitely singularity even for finite size system, since non-Hermiticity endow many-body system with different singular behavior from classical phase transition. Moreover our results show that the phase transition have no counterpart in Hermitian case and belongs to completely different universality class.
The contact process is a paradigmatic example of nonequilibrium dynamics, with broad applications ranging from chemistry to sociology. Its quantum counterpart, the quantum contact process (QCP), extends the classical model to include coherent processes. Despite sustained interest, the nature of the transition in the one-dimensional (1D) QCP remains debatable. Here, combining Liouvillian spectral analysis, the tensor jump method, exact quantum jump Monte Carlo, and truncated Wigner simulations, we show that 1D QCP undergoes a continuous absorbing-state phase transition, with critical exponents distinct from the classical case. We further find Liouvillian gap closes well below the critical point, highlighting that spectral gap analysis alone cannot distinguish a phase transition from metastability in the QCP. Crucially, the 1D QCP is weakly entangled, yet even this weak entanglement is indispensable for capturing the correct critical behavior, whereas semiclassical methods artificially stabilize the active state and predict a spurious first-order transition. Our work establishes the quantum origin of the phase transition in the 1D QCP and underscores the essential role of entanglement in dissipative quantum many-body systems.
Theoretical analysis of a prototypical two-qubit effective non-Hermitian system characterized by asymmetric Heisenberg XY interactions in the absence of external magnetic fields demonstrates that maximal bipartite entanglement and quantum phase transitions can be induced exclusively through non-Hermiticity. At thermal equilibrium as T→0, the system attains maximal entanglement C=1 for values of the non-Hermiticity parameter greater than a critical value γ>γc=J(1−δ2), where J denotes the exchange interaction and δ represents the anisotropy of the system; conversely, for γ<γc, entanglement is nonmaximal and given by C=(1−(γ/J)2). The entanglement undergoes a discontinuous transition to zero precisely at γ=γc. This phase transition originates from the closing of the energy gap at a non-Hermiticity-driven ground state degeneracy, which is fundamentally different from an exceptional point. This work suggests the use of singular-value-decomposition generalized density matrix for the computation of entanglement in bi-orthogonal systems.
Quantum phase transitions occur in non-Hermitian systems. In this work we show that density functional theory, for the first time, uncovers universal critical behaviors for quantum phase transitions and quantum entanglement in non-Hermitian many-body systems. To be specific, we first prove that the non-degenerate steady state of a non-Hermitian quantum many body system is a universal function of the first derivative of the steady state energy with respect to the control parameter. This finding has far-reaching consequences for non-Hermitian systems. First, it bridges the non-analytic behavior of physical observable and no-analytic behavior of steady state energy, which explains why the quantum phase transitions in non-Hermitian systems occur for finite systems. Second, it predicts universal scaling behaviors of any physical observable at non-Hermitian phase transition point with scaling exponent being (1 - 1/p) with p being the number of coalesced states at the exceptional point. Third, it reveals that quantum entanglement in non-Hermitian phase transition point presents universal scaling behaviors with critical exponents being (1 - 1/p). These results uncover universal critical behaviors in non-Hermitian phase transitions and provide profound connections between entanglement and phase transition in non-Hermitian quantum many-body physics.
The contact process is a paradigmatic classical stochastic system displaying critical behavior even in one dimension. It features a nonequilibrium phase transition into an absorbing state that has been widely investigated and shown to belong to the directed percolation universality class. When the same process is considered in a quantum setting, much less is known. So far, mainly semiclassical studies have been conducted and the nature of the transition in low dimensions is still a matter of debate. Also, from a numerical point of view, from which the system may look fairly simple-especially in one dimension-results are lacking. In particular, the presence of the absorbing state poses a substantial challenge, which appears to affect the reliability of algorithms targeting directly the steady state. Here we perform real-time numerical simulations of the open dynamics of the quantum contact process and shed light on the existence and on the nature of an absorbing state phase transition in one dimension. We find evidence for the transition being continuous and provide first estimates for the critical exponents. Beyond the conceptual interest, the simplicity of the quantum contact process makes it an ideal benchmark problem for scrutinizing numerical methods for open quantum nonequilibrium systems.
Abstract Continuous phase transition in quantum matters is a significant issue in condensed matter physics. In general, the continuous quantum phase transitions in many-body systems occur with gap closing. On the other hand, non-Hermitian systems could display quite different properties as their Hermitian counterparts. In this paper, we show that a hidden, continuous quantum phase transition occurs without gap closing in non-Hermitian transverse Ising model. By using a projected Jordan–Wigner transformation, the one-dimensional (1D) non-Hermitian transverse Ising model with ferromagnetic order is mapped on to 1D non-Hermitian Kitaev model with topological superconducting order and becomes exactly solvable. A hidden, continuous quantum phase transition is really normal–abnormal transition for fermionic correlation in the 1D non-Hermitian Kitaev model. In addition, similar hidden, continuous quantum phase transition is discovered in two-dimensional non-Hermitian transverse Ising model and thus becomes a universal feature in certain non-Hermitian many-body systems.
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 investigated by the second derivative of the 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.