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Scaling of geometric phase close to multicritical points in cluster-Ising models

Wei Nie, Feng Mei, Luigi Amico A, L. C. Kwek

Published Feb 8, 2017• 0 citations
OpenAlex

Abstract

We study the phase diagram of a class of models in which a generalized cluster interaction can be quenched by Ising exchange interaction and external magnetic field. We characterize the various phases through winding numbers. They may be ordinary phases with local order parameter or exotic ones, known as symmetry protected topologically ordered phases. Quantum phase transitions with dynamical critical exponents z = 1 or z = 2 are found. Quantum phase transitions are analyzed through finite-size scaling of the geometric phase accumulated when the spins of the lattice perform an adiabatic precession. In particular, we quantify the scaling behavior of the geometric phase in relation with the topology and low energy properties of the band structure of the system.

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We study the phase diagram of a class of models in which a generalized cluster interaction can be quenched by Ising exchange interaction and external magnetic field. We characterize the various phases through winding numbers. They may be ordinary phases with local order parameter or exotic ones, known as symmetry protected topologically ordered phases. Quantum phase transitions with dynamical critical exponents z = 1 or z = 2 are found. Quantum phase transitions are analyzed through finite-size scaling of the geometric phase accumulated when the spins of the lattice perform an adiabatic precession. In particular, we quantify the scaling behavior of the geometric phase in relation with the topology and low energy properties of the band structure of the system.
We study the phase diagram of a class of models in which a generalized cluster interaction can be quenched by an Ising exchange interaction and external magnetic field. The various phases are studied through winding numbers. They may be ordinary phases with local order parameters or exotic ones, known as symmetry protected topologically ordered phases. Quantum phase transitions with dynamical critical exponents z=1 or z=2 are found. In particular, the criticality is analyzed through finite-size scaling of the geometric phase accumulated when the spins of the lattice perform an adiabatic precession. With this study, we quantify the scaling behavior of the geometric phase in relation to the topology and low-energy properties of the band structure of the system.
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.
We study the dynamical quantum phase transitions (DQPTs) manifested in the subsequent unitary dynamics of an extended Ising model with an additional three spin interactions following a sudden quench. Revisiting the equilibrium phase diagram of the model, where different quantum phases are characterized by different winding numbers, we show that in some situations the winding number may not change across a gap closing point in the energy spectrum. Although, usually there exists a one-to-one correspondence between the change in winding number and the number of critical time scales associated with DQPTs, we show that the extended nature of interactions may lead to unusual situations. Importantly, we show that in the limit of the cluster Ising model, three critical modes associated with DQPTs become degenerate, thereby leading to a single critical time scale for a given sector of Fisher zeros.
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.
By constructing an exactly solvable spin model, we investigate the critical behaviors of transverse-field Ising chains interpolated with cluster interactions, which exhibit various types of topologically distinct Ising critical points. Using fidelity susceptibility as an indicator, we establish the global phase diagram, including ferromagnetic, trivial paramagnetic, and symmetry-protected topological phases. Different types of critical points exist between these phases, encompassing both topologically trivial and nontrivial Ising critical points, as well as Gaussian critical points. Importantly, we demonstrate the existence of a Lifshitz transition between these topologically distinct Ising critical points, with central charge and critical exponents determined through finite-size scaling. This work serves as a valuable reference for further research on phase transitions within the gapless quantum phase of matter.
We study the ground-state properties of a spin-1/2 model on a chain containing four-spin Ising-like interactions in the presence of both transverse and longitudinal magnetic fields. We use entanglement entropy and finite-size scaling methods to obtain the phase diagrams of the model. Our numerical calculations reveal a rich variety of phases and the existence of multicritical points in the system. We identify phases with both ferromagnetic and antiferromagnetic orderings. We also find periodically modulated orderings formed by a cluster of like spins followed by another cluster of opposite like spins. The quantum phases in the model are found to be separated by either first- or second-order transition lines.