Related papers: Topological Classification of Gapped Spin Chains :…
We propose a systematic wave function based approach to construct topological invariants for families of lattice systems that are short-range entangled using local parameter spaces. This construction is particularly suitable when given a…
We study quantized non-local order parameters, constructed by using partial time-reversal and partial reflection, for fermionic topological phases of matter in one spatial dimension protected by an orientation reversing symmetry, using…
We present a quantized non-Abelian Berry phase for time reversal invariant systems such as quantum spin Hall effect. Ordinary Berry phase is defined by an integral of Berry's gauge potential along a loop (an integral of the Chern-Simons…
We derive the general formula giving the Berry phase for an arbitrary spin, having both magnetic-dipole and electric-quadrupole couplings with external time-dependent fields. We assume that the effective E and B fields remain orthogonal…
We show that the entanglement spectrum can be used to define non-local order in gapless spin systems. We find a gap that fully separates a series of generic, high `entanglement energy' levels, from a flat band of levels with specific…
The Berry phase, a fundamental geometric phase in quantum systems, has become a crucial tool for probing the topological properties of materials. Quantum oscillations, such as Shubnikov-de Haas (SdH) oscillations, are widely used to extract…
Symmetry protected quantization of the Berry phase is discussed in relation to edge states. Assuming an existence of some adiabatic process which protects quantization of the Berry phase, non trivial Berry phase $\gamma=\pm 2\pi\rho$…
Topological phases and materials have attracted much attention in recent years. Though many progress has been made, the effect of nonlinearity on such system remains untouched. In this paper, by considering the mean-field approximation in a…
We study the connection between Berry phases and quantum phase transitions of generic quantum many-body systems. Consider sequences of Berry phases associated to sequences of loops in the parameter space whose limit is a point. If the…
A large class of quantum phase transitions for quantum lattice systems are characterized by local order parameters. It is shown that local order parameters may be systematically constructed from tensor network representations of quantum…
We consider a one-dimensional, time-reversal-invariant system with attractive interactions and spin-orbit coupling. Such a system is gapless due to the strong quantum fluctuations of the superconducting order parameter. However, we show…
We have studied the $Z_2$ topological number defined by the Berry phase for the gapped frustrated systems including the orthogonal dimer model which has a direct product state of local quantum clusters as the exact ground state. The $Z_2$…
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,…
It has been recently proposed that the reduced density matrix may be used to derive the order parameter of a condensed matter system. Here we propose order parameters for the phases of a topological insulator, specifically a spinless…
The theoretical identification of crystalline topological materials has enjoyed sustained success in simplified materials models, often by singling out discrete symmetry operations protecting the topological phase. When band structure…
We consider the classification problem of symmetry protected topological (SPT) phases on quantum spin systems. SPT phases are gapped short-range-entangled quantum phases with a symmetry $G$. We explain that in one and two-dimensional…
We propose an order parameter to characterize valence-bond-solid (VBS) states in quantum spin chains, given by the ground-state expectation value of a unitary operator appearing in the Lieb-Schultz-Mattis argument. We show that the order…
Non-Abelian and non-adiabatic variants of Berry's geometric phase have been pivotal in the recent advances in fault tolerant quantum computation gates, while Berry's phase itself is at the heart of the study of topological phases of matter.…
A topological insulator is characterized by spin-momentum locking on its boundary. The spin momentum locking on the surface of a three dimensional topological insulator leads to the existence of a non-trivial Berry's phase which leads to…
The quantum critical properties of the sub-Ohmic spin-1/2 spin-boson model and of the Bose-Fermi Kondo model have recently been discussed controversially. The role of the Berry phase in the breakdown of the quantum-to-classical mapping of…