Related papers: Phase Space Entanglement Spectrum
Freed-Hopkins give a mathematical ansatz for classifying gapped invertible phases of matter with a spatial symmetry in terms of Borel-equivariant generalized homology. We propose a slight generalization of this ansatz to account for cases…
The phase diagram of spins 1/2 embedded in a magnetic field mutually interacting antiferromagnetically is determined. Contrary to the ferromagnetic case where a second order quantum phase transition occurs, a first order transition is…
Harmonic oscillator, in 2-dimensional noncommutative phase space with non-vanishing momentum-momentum commutators, is studied using an algebraic approach. The corresponding eigenvalue problem is solved and discussed.
We introduce a systematic framework to calculate the bipartite entanglement entropy of a spatial subsystem in a one-dimensional quantum gas which can be mapped into a noninteracting fermion system. To show the wide range of applicability of…
We investigate further the relationship between the entanglement spectrum of a composite many-body system and the energy spectrum of a subsystem making use of concepts of canonical thermodynamics. In many important cases the entanglement…
Using the phase-space formulation of quantum mechanics, we derive a four-component Wigner equation for a system composed of spin-1/2 fermions (typically, electrons) including the Zeeman effect and the spin-orbit coupling. This Wigner…
We consider a six-parameter family of the square integrable wave functions for the simple harmonic oscillator, which cannot be obtained by the standard separation of variables. They are given by the action of the corresponding maximal…
We investigate the entanglement spectra of topological insulators which manifest edge states on a lattice with spatial boundaries. In the physical energy spectrum, a subset of the edge states that intersect the Fermi level translates to…
Quantum entanglement occurs not just in discrete systems such as spins, but also in the spatial wave functions of systems with more than one degree of freedom. It is easy to introduce students to entangled wave functions at an early stage,…
We examine several well known quantum spin models and categorize behavior of pairwise entanglement at quantum phase transitions. A unified picture on the connection between the entanglement and quantum phase transition is given.
The entanglement spectrum describing quantum correlations in many-body systems has been recently recognized as a key tool to characterize different quantum phases, including topological ones. Here we derive its analytically scaling…
Topological phases are characterized by their entanglement properties, which is manifest in a direct relation between entanglement spectra and edge states discovered by Li and Haldane. We propose to leverage the power of synthetic quantum…
We formulate and argue in favor of the following conjecture: There exists an intimate connection between Wigner's quantum mechanical phase space distribution function and classical Fresnel optics.
Topological phases of matter are traditionally characterized through symmetry-based classifications. In cases of symmetry breaking, the projected spectrum - obtained by projecting the ground state onto the eigenstates of a pertinent quantum…
We study the separability of permutationally symmetric quantum states. We show that for bipartite symmetric systems most of the relevant entanglement criteria coincide. However, we provide a method to generate examples of bound entangled…
A many-body wave function can be factorized in Fock space into a marginal amplitude describing a set of strongly correlated orbitals and a conditional amplitude for the remaining weakly correlated part. The marginal amplitude is the…
We present a novel extension of the concept of scars for the wave functions of classically chaotic few-body systems of identical particles with rotation and permutation symmetry. Generically there exist manifolds in classical phase space…
We study the localization of particles rotating in a two-dimensional harmonic potential by solving their rotational spectrum using many-particle quantum mechanics and comparing the result to that obtained with quantizing the rigid rotation…
We derive a two-dimensional symplectic map for particle motion at the plasma edge by modeling the electrostatic potential as a superposition of integer spatial harmonics with relative phase shift, then reduce it to a two-wave model to study…
It is shown that the Husimi representations of chaotic eigenstates are strongly correlated along classical trajectories. These correlations extend across the whole system size and, unlike the corresponding eigenfunction correlations in…