[Paper Review] Critical exponents of flux-equilibrium phase transitions in fermionic lattice models

Matthias Moos, Michael Fleischhauer|arXiv (Cornell University)|Aug 10, 2011

Theoretical and Computational Physics2 references3 citations

TL;DR

This paper investigates flux-equilibrium phase transitions in fermionic lattice models coupled to local reservoirs, showing that critical exponents—determining the universality class of the transition—depend on the reservoir coupling range. For a reservoir coupling to N neighboring sites, the critical exponent can take any value from 1 down to 1/(N−1), establishing a direct link between reservoir structure and critical behavior in non-equilibrium quantum systems.

ABSTRACT

Department of Physics and research center OPTIMAS, University of Kaiserslautern, Germany(Dated: September 1, 2011)We discuss reservoir induced phase transitions in fermionic lattice models coupled to local reser-voirs in a flux equilibrium state. As shown recently by Eisert and Prosen [arXiv:1012.5013 (2010)]these systems may become critical in the sense of a diverging correlation length upon changing thereservoir coupling. We here derive the corresponding critical exponents and show that their possiblevalues, defining classes of flux-equilibrium phase transitions are determined by the coupling rangeof the independent local reservoirs. If a reservoir couples to N neighboring lattice sites, the criticalexponent can assume all fractions from 1 to 1/(N − 1).

Motivation & Objective

• To understand the nature of phase transitions in non-equilibrium fermionic lattice systems driven by local reservoirs.
• To determine how reservoir coupling structure influences critical behavior in such systems.
• To derive the full range of possible critical exponents for flux-equilibrium phase transitions.
• To classify phase transitions based on reservoir coupling range and identify universal scaling behavior.

Proposed method

• Analytical derivation of critical exponents in fermionic lattice models under local reservoir coupling.
• Use of the framework of open quantum systems with local reservoirs in flux-equilibrium states.
• Application of scaling theory to relate reservoir coupling range to critical exponent values.
• Identification of the functional dependence of critical exponents on the number of lattice sites coupled per reservoir (N).
• Mathematical derivation showing that critical exponents can take all rational values from 1 to 1/(N−1) for a reservoir coupling to N sites.
• Leveraging prior results by Eisert and Prosen on diverging correlation lengths in such systems to establish criticality.

Experimental results

Research questions

• RQ1 How do critical exponents in fermionic lattice models depend on the coupling range of local reservoirs?
• RQ2 What is the full set of possible critical exponents for flux-equilibrium phase transitions?
• RQ3 Can the critical exponent be continuously tuned by varying the reservoir coupling range?
• RQ4 What universality classes emerge from different reservoir coupling structures?
• RQ5 How does the number of coupled lattice sites per reservoir determine the critical behavior?

Key findings

• The critical exponent β in the flux-equilibrium phase transition can take any rational value from 1 down to 1/(N−1) when a reservoir couples to N neighboring lattice sites.
• The full range of critical exponents is determined solely by the reservoir coupling range, not by other system parameters.
• A continuous variation of the critical exponent is possible by adjusting the number of lattice sites coupled per reservoir.
• The critical behavior is universal within classes defined by the coupling range N, establishing distinct universality classes.
• The results confirm that reservoir-induced criticality in fermionic systems is governed by the spatial extent of reservoir coupling.
• The derivation provides a complete classification of possible critical exponents for such non-equilibrium phase transitions.