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arXiv:2203.07784 · Physical Review A

Emergent phase transitions in a cluster Ising model with dissipation

Zheng-Xin Guo, Xue-Jia Yu, Xi-Dan Hu, Zhi Li

Published May 27, 2022• 43 citations
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Abstract

We study a cluster Ising model with non-Hermitian external field which can be exactly solved in the language of free fermions. By investigating the second derivative of energy density and fidelity, the possible new critical points are tentatively located. The string order parameter and staggered magnetization are then detected to reveal emergent phases of brand new characteristics. To categorize the exotic phases and phase transitions induced by non-Hermiticity, we calculate the variation mode of the spin-correlation function as well as of the string correlation function, which characterize the emergent phases and critical points with different patterns of decay and critical exponents. With the help of the string order parameter and staggered magnetization, we find that there are four phases after introducing the non-Hermiticity---the cluster phase, the gapless phase, the paramagnetic phase, and the antiferromagnetic phase. A phase diagram is then presented to graphically illustrate, based on two ``Kosterlitz-Thouless-like'' phase transitions and an Ising phase transition, respectively, the generation of three critical lines as non-Hermitian strength increases. Our theoretical work is expected to be realized in the experiment of ultracold atoms, pushing for progress in exploring novel phases and phase transitions.

DOI
10.1103/physreva.105.053311

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We study a cluster Ising model with non-Hermitian external field which can be exactly solved in the language of free fermions. By investigating the second derivative of energy density and fidelity, the possible new critical points are tentatively located. The string order parameter and staggered magnetization are then detected to reveal emergent phases of brand new characteristics. To categorize the exotic phases and phase transitions induced by non-Hermiticity, we calculate the variation mode of the spin-correlation function as well as of the string correlation function, which characterize the emergent phases and critical points with different patterns of decay and critical exponents. With the help of the string order parameter and staggered magnetization, we find that there are four phases after introducing the non-Hermiticity---the cluster phase, the gapless phase, the paramagnetic phase, and the antiferromagnetic phase. A phase diagram is then presented to graphically illustrate, based on two ``Kosterlitz-Thouless-like'' phase transitions and an Ising phase transition, respectively, the generation of three critical lines as non-Hermitian strength increases. Our theoretical work is expected to be realized in the experiment of ultracold atoms, pushing for progress in exploring novel phases and phase transitions.
We study the ground-state phase diagram of a non-Hermitian cluster-XYXYXY spin chain in the language of free fermions. By calculating the second derivative of ground-state energy density and various types of order parameters, we establish the global ground-state phase diagram of the model, exhibiting rich quantum phases and corresponding phase transitions. Specifically, the results reveal that the non-Hermitian cluster-XYXYXY model contains five different phases and two critical regions, i.e., ferromagnetic (FM), antiferromagnetic (AFM), symmetry-protected topological (SPT), paramagnetic (PM), Luttinger liquid-like phase, as well as critical regions I and II. The order parameters and critical behaviors are investigated and the correctness of the theory is confirmed.
Abstract We perform a comprehensive analytical study of the exotic quantum phases and phase transitions emerging from the cluster-Ising model with off-diagonal Gamma interactions. Specifically, we map out the ground-state phase diagram by analyzing both local and nonlocal order parameters, together with the energy spectra. The results reveal one pair of gapped phases—namely antiferromagnetic (AFM) long-range ordered phase and symmetry-protected topological (SPT) phase—as well as two distinct gapless spiral phases induced by the off-diagonal interactions. Remarkably, the phase diagram contains four distinct transition lines. Two of them, separating different gapped or gapless phases, are governed by the Ising and three-copy Ising conformal field theories, respectively. In contrast, the remaining two transition lines—between the gapless spiral and gapped phases—belong to a non-conformal Lifshitz criticality with dynamical critical exponent z=2z = 2z=2 z = 2 . More importantly, the intersection of these four transition lines gives rise to a new Lifshitz multicritical point exhibiting emergent conformal symmetry, marking a fundamental departure from all previously known non-conformal Lifshitz points. This work provides a valuable reference for future investigations of exotic gapless phases and their transitions in exactly solvable many-body systems.
We study a Hamiltonian system describing a three-spin-1/21/21/2 clusterlike interaction competing with an Ising-like antiferromagnetic interaction. We compute free energy, spin-correlation functions, and entanglement both in the ground and in thermal states. The model undergoes a quantum phase transition between an Ising phase with a nonvanishing magnetization and a cluster phase characterized by a string order. Any two-spin entanglement is found to vanish in both quantum phases because of a nontrivial correlation pattern. Nevertheless, the residual multipartite entanglement is maximal in the cluster phase and dependent on the magnetization in the Ising phase. We study the block entropy at the critical point and calculate the central charge of the system, showing that the criticality of the system is beyond the Ising universality class.
In this work we study non-Hermitian extensions of the paradigmatic spin-1/2 XY chain in a magnetic field. Using the mapping of the model to free fermion form, we provide analytical insights into the energy spectrum of the non-Hermitian model and establish an intrinsic connection between the quasienergies and topological invariants. We also use exact diagonalization as a supplementary method to examine the performance of biorthogonal-based expectation values. Our results confirm that the theoretical analysis is consistent with the numerical results, with the extended phase diagram determined via the analytical solution and the critical behavior of the fidelity and entanglement. The entanglement transition goes hand in hand with the non-Hermitian topological phase transition. Like the Hermitian case, we analyze the critical behavior using finite-size scaling. Our results show that non-Hermiticity can induce the system into a new universality class with unusual critical exponent. We also emphasize the ability of the Loschmidt echo to characterize potential phase transitions and introduce the average of the Loschmidt echo to describe phase transitions in non-Hermitian systems.
We investigate the cluster Ising chain with an additional nearest-neighbor interaction using tensor-network methods and a weak-coupling field theory. Without the interaction, the Jordan-Wigner transformation decomposes the model into a triplet of identical Majorana chains related by an exact O(3)O(3)O(3) flavor symmetry. Their common mass vanishes at the SU(2)2SU(2)_2SU(2)2​ Wess-Zumino-Novikov-Witten critical point with central charge c=3/2c = 3/2c=3/2 separating the symmetry-protected topological cluster phase from a ferromagnet. The interaction reduces O(3)O(3)O(3) to its cyclic subgroup C3C_3C3​, splitting the triplet into a singlet and a doublet whose gaps close separately, producing a critical bifurcation into Ising (c=1/2c = 1/2c=1/2) and Gaussian (c=1c = 1c=1) critical lines. A second ferromagnetic phase opens between these critical lines for repulsive interactions and a disordered phase for attractive ones. The Gaussian line then separates two Landau-incompatible ferromagnets, realizing a deconfined quantum critical line with emergent O(2)O(2)O(2) symmetry, along which our independently extracted exponents vary continuously yet satisfy the parameter-free relation β=(2ν−1)/4β= (2ν- 1)/4β=(2ν−1)/4 of the eight-vertex weak universality class. At stronger repulsion this line opens into an extended gapless floating phase with incommensurate algebraic correlations, entered through Berezinskii-Kosterlitz-Thouless transitions. All of these phases and the transitions between them are captured by the weak-coupling theory. Beyond its regime of validity, our simulations reveal a translation-symmetry-breaking antiferromagnet reached through first-order transitions.
We study a cluster Ising model with multispin interactions which can be exactly solved in the framework of free fermions. The model can realize topological phases with any integer winding numbers; we study the critical and multicritical behaviors of the phase transitions between these topological phases. For the ordinary critical point, we find that the critical exponent that governs the divergence of the correlation length is ν=1, and the critical exponent that describes the scaling behaviors of the order parameter is β=ΔN_{w}/8, with ΔN_{w} the difference of the winding numbers of the two phases at the two sides of the critical point. However, these results are not applicable for some multicritical points which have much more complicated behaviors, such as path dependent scaling behaviors and quasicritical behaviors and so forth.