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We present a software package DiracQ, for use in quantum many-body Physics. It is designed for helping with typical algebraic manipulations that arise in quantum Condensed Matter Physics and Nuclear Physics problems, and also in some subareas of Chemistry. DiracQ is invoked within a Mathematica session, and extends the symbolic capabilities of Mathematica by building in standard commutation and anticommutation rules for several objects relevant in many-body Physics. It enables the user to carry out computations such as evaluating the commutators of arbitrary combinations of spin, Bose and Fermi operators defined on a discrete lattice, or the position and momentum operators in the continuum. Some examples from popular systems, such as the Hubbard model, are provided to illustrate the capabilities of the package.
A gapped many-body system is described by path integral on a space-time lattice $C^{d+1}$, which gives rise to a partition function $Z(C^{d+1})$ if $partial C^{d+1} =emptyset$, and gives rise to a vector $|Psirangle$ on the boundary of space-time if
A numerical bootstrap method is proposed to provide rigorous and nontrivial bounds in general quantum many-body systems with locality. In particular, lower bounds on ground state energies of local lattice systems are obtained by imposing positivity c
We study a kinetically constrained pair hopping model that arises within a Landau level in the quantum Hall effect. At filling $ u = 1/3$, the model exactly maps onto the so-called PXP model, a constrained model for the Rydberg atom chain that is num
Characterizing states of matter through the lens of their ergodic properties is a fascinating new direction of research. In the quantum realm, the many-body localization (MBL) was proposed to be the paradigmatic ergodicity breaking phenomenon, which
We show that the magnetization of a single `qubit spin weakly coupled to an otherwise isolated disordered spin chain exhibits periodic revivals in the localized regime, and retains an imprint of its initial magnetization at infinite time. We demonstr