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Register a new userA quantum topological phase transition at the microscopic level
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Authors
C. Castelnovo
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We study a quantum phase transition between a phase which is topologically ordered and one which is not. We focus on a spin model, an extension of the toric code, for which we obtain the exact ground state for all values of the coupling constant that takes the system across the phase transition. We compute the entanglement and the topological entropy of the system as a function of this coupling constant, and show that the topological entropy remains constant all the way up to the critical point, and jumps to zero beyond it. Despite the jump in the topological entropy, the transition is second order as detected via any local observable.
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Fracton topological order (FTO) is a new classification of correlated phases in three spatial dimensions with topological ground state degeneracy (GSD) scaling up with system size, and fractional excitations which are immobile or have restricted mobility. With the topological origin of GSD, FTO is immune to local perturbations, whereas a strong enough global external perturbation is expected to break the order. The critical point of the topological transition is however very challenging to identify. In this work, we propose to characterize quantum phase transition of the type-I FTOs induced by external terms and develop a theory to study analytically the critical point of the transition. In particular, for the external perturbation term creating lineon-type excitations, we predict a generic formula for the critical point of the quantum phase transition, characterized by the breaking-down of GSD. This theory applies to a board class of FTOs, including X-cube model, and for more generic FTO models under perturbations creating two-dimensional (2D) or 3D excitations, we predict the upper and lower limits of the critical point. Our work makes a step in characterizing analytically the quantum phase transition of generic fracton orders.
We consider a system of mutually interacting spin 1/2 embedded in a transverse magnetic field which undergo a second order quantum phase transition. We analyze the entanglement properties and the spin squeezing of the ground state and show that, contrarily to the one-dimensional case, a cusp-like singularity appears at the critical point $lambda_c$, in the thermodynamic limit. We also show that there exists a value $lambda_0 geq lambda_c$ above which the ground state is not spin squeezed despite a nonvanishing concurrence.
To harness technological opportunities arising from optically controlled quantum many-body states a deeper theoretical understanding of driven-dissipative interacting systems and their nonequilibrium phase transitions is essential. Here we provide numerical evidence for a dynamical phase transition in the nonequilibrium steady state of interacting magnons in the prototypical two-dimensional Heisenberg antiferromagnet with drive and dissipation. This nonthermal transition is characterized by a qualitative change in the magnon distribution, from subthermal at low drive to a generalized Bose-Einstein form including a nonvanishing condensate fraction at high drive. A finite-size analysis reveals static and dynamical critical scaling, with a discontinuous slope of the magnon number versus driving field strength and critical slowing down at the transition point. Implications for experiments on quantum materials and polariton condensates are discussed.
A number of tools have been developed to detect topological phase transitions in strongly correlated quantum systems. They apply under different conditions, but do not cover the full range of many-body models. It is hence desirable to further expand the toolbox. Here, we propose to use quasiparticle properties to detect quantum phase transitions. The approach is independent from the choice of boundary conditions, and it does not assume a particular lattice structure. The probe is hence suitable for, e.g., fractals and quasicrystals. The method requires that one can reliably create quasiparticles in the considered systems. In the simplest cases, this can be done by a pinning potential, while it is less straightforward in more complicated systems. We apply the method to several rather different examples, including one that cannot be handled by the commonly used probes, and in all the cases we find that the numerical costs are low. This is so, because a simple property, such as the charge of the anyons, is sufficient to detect the phase transition point. For some of the examples, this allows us to study larger systems and/or further parameter values compared to previous studies.
A local Hamiltonian with Topological Quantum Order (TQO) has a robust ground state degeneracy that makes it an excellent quantum memory candidate. This memory can be corrupted however if part of the state leaves the protected ground state manifold and returns later with a dynamically accrued phase error. Here we analyse how TQO suppresses this process and use this to quantify the degree to which spectral densities in different topological sectors are correlated. We provide numerical verification of our results by modelling an interacting p-wave superconducting wire.
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