Broken-Hermiticity phase transition in the Bose-Hubbard model

Kód výsledku v IS VaVaI

RIV/61389005:_____/18:00496797 - isvavai.cz

Výsledek na webu

http://dx.doi.org/10.1103/PhysRevA.98.052102

DOI - Digital Object Identifier

10.1103/PhysRevA.98.052102

Jazyk výsledku

angličtina

Název v původním jazyce

Broken-Hermiticity phase transition in the Bose-Hubbard model

Popis výsledku v původním jazyce

For the two-mode and (N - 1 )-bosonic Bose-Hubbard quantum system a less usual phase transition controlled by the parameters representing the on-site energy difference is studied. In the literature the parameter is considered either real (epsilon > 0) or purely imaginary (with, say, gamma = Im epsilon > 0), so the phase transition is analyzed here at the interface epsilon = gamma = 0. The evolution in the gamma-controlled phase is required unitary so that the main task for the theory is found in the (quasi-)Hermitization of the Hamiltonian, achieved by a suitable amendment of the inner product in Hilbert space, <.vertical bar.> -> <.vertical bar Theta vertical bar.>. In the most relevant domain of small gamma the linearized Hilbert-space metric Theta(gamma) [constrained by the requirement lim(gamma -> 0) Theta(gamma) = I of the smoothness of the change of the Hilbert space at the phase transition] is constructed in closed form. Beyond the phase-transition instant, several forms of the systematic non-numerical recurrent construction of the exact metrics Theta(gamma) are also shown user friendly and feasible, at the not too large matric dimensions N at least.

Název v anglickém jazyce

Broken-Hermiticity phase transition in the Bose-Hubbard model

Popis výsledku anglicky

For the two-mode and (N - 1 )-bosonic Bose-Hubbard quantum system a less usual phase transition controlled by the parameters representing the on-site energy difference is studied. In the literature the parameter is considered either real (epsilon > 0) or purely imaginary (with, say, gamma = Im epsilon > 0), so the phase transition is analyzed here at the interface epsilon = gamma = 0. The evolution in the gamma-controlled phase is required unitary so that the main task for the theory is found in the (quasi-)Hermitization of the Hamiltonian, achieved by a suitable amendment of the inner product in Hilbert space, <.vertical bar.> -> <.vertical bar Theta vertical bar.>. In the most relevant domain of small gamma the linearized Hilbert-space metric Theta(gamma) [constrained by the requirement lim(gamma -> 0) Theta(gamma) = I of the smoothness of the change of the Hilbert space at the phase transition] is constructed in closed form. Beyond the phase-transition instant, several forms of the systematic non-numerical recurrent construction of the exact metrics Theta(gamma) are also shown user friendly and feasible, at the not too large matric dimensions N at least.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

Projekt

GA16-22945S: Kvantová Wheelerova – DeWittova rovnice a její unitárně evoluční interpretace

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Physical Review A

ISSN

2469-9926

e-ISSN

—

Svazek periodika

98

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

12

Strana od-do

—

Kód UT WoS článku

000449292200001

EID výsledku v databázi Scopus

2-s2.0-85056340389