相关论文: Scaling Theory of Topological Phase Transitions

Distinct from the dynamical phase, in a cyclic evolution, a system's state may acquire an additional component, a.k.a. geometric phase. The latter is a manifestation of a closed path in state space. Geometric phases underlie various…

Topology is being widely adopted to understand and to categorize quantum matter in modern physics. The nexus of topology orders, which engenders distinct quantum phases with benefits to both fundamental research and practical applications…

Topology forms a cornerstone in modern condensed matter and statistical physics, offering a new framework to classify the phases and phase transitions beyond the traditional Landau paradigm. However, it is widely believed that topological…

The quantum phase diagram of the Hubbard chain with correlated hopping is accurately determined through jumps in $\pi$ in the charge and spin Berry phases. The nature of each thermodynamic phase, and the existence of charge and spin gaps,…

We discuss different properties and the ability of several topological invariants based on position operators to identify phase transitions, and compare with more accurate methods, like crossing of excited energy levels and jumps in Berry…

In the modern theory of polarization, polarization itself is given by a geometric phase. In calculations for interacting systems the polarization and its variance are obtained from the polarization amplitude. We interpret this quantity as a…

This paper is concerned with the physics of parametrized gapped quantum many-body systems, which can be viewed as a generalization of conventional topological phases of matter. In such systems, rather than considering a single Hamiltonian,…

The relation between thermodynamic phase transitions in classical systems and topological changes in their configuration space is discussed for two physical models and contains the first exact analytic computation of a topologic invariant…

In a variety of systems which exhibit aging, the two-time response function scales as $R(t,s)\approx s^{-1-a} f(t/s)$. We argue that dynamical scaling can be extended towards conformal invariance, obtaining thus the explicit form of the…

The topology of the non-adiabatic parameter space bundle is discussed for evolution of exact cyclic state vectors in Berry's original example of split angular momentum eigenstates. It turns out that the change in topology occurs at a…

A celebrated and controversial hypothesis conjectures that some biological systems --parts, aspects, or groups of them-- may extract important functional benefits from operating at the edge of instability, halfway between order and…

In this paper, we investigate signatures of topological phase transitions in interacting systems. We show that the key signature is the existence of a topologically protected level crossing, which is robust and sharply defines the…

Quantum geometry characterizes the variation of wavefunctions in momentum space through their overlaps and relative phases, providing a general framework for understanding many transport and optical properties. It is generally formulated in…

We discuss a cluster-like 1D system with triplet interaction. We study the topological properties of this system. We find that the degeneracy depends on the topology of the system, and well protected against external local perturbations.…

We study the many-body physics of different quantum systems using a hierarchy of correlations, which corresponds to a generalization of the $1/\mathcal{Z}$ hierarchy. The decoupling scheme obtained from this hierarchy is adapted to…

At a continuous transition into a nonunique absorbing state, particle systems may exhibit nonuniversal critical behavior, in apparent violation of hyperscaling. We propose a generalized scaling theory for dynamic critical behavior at a…

Topological quantum phase transitions are characterised by changes in global topological invariants. These invariants classify many body systems beyond the conventional paradigm of local order parameters describing spontaneous symmetry…

We propose a new theory to characterize equilibrium topological phase with non-equilibrium quantum dynamics by introducing the concept of high-order topological charges, with novel phenomena being predicted. Through a dimension reduction…

Dynamical universality plays a fundamental role in understanding the scaling properties of critical dynamics, including absorbing phase transitions and physical aging. Although individual universality classes have been extensively studied,…

The well known scaling laws relating critical exponents in a second order phase transition have been generalized to the case of an arbitrarily higher order phase transition. In a higher order transition, such as one suggested for the…