Abstract
We study the connection between the exponent of the order parameter of the Mott insulator-to-superfluid transition occurring in the two-dimensional Bose–Hubbard model, and the divergence exponents of its one- and two-particle correlation functions. We find that at the multicritical points all divergence exponents are related to each other, allowing us to express the critical exponent in terms of one single divergence exponent. This approach correctly reproduces the critical exponent of the three-dimensional XY universality class. Because divergence exponents can be computed in an efficient manner by hypergeometric analytic continuation, our strategy is applicable to a wide class of systems.
Highlights
Continuous phase transitions are often described by Landau’s approach [1,2,3,4,5]: assume that the thermodynamical potential Γ of a given system possesses the formG = a0 + a2y2 + a4y4, (1)where the coefficients a0, a2, a4 depend on a control parameter j, and the system adopts, for each fixed value of j, that value ymin of ψ for which the potential (1) takes on its minimum
When trying to reconcile this existing knowledge with an approach based on an effective potential (1), one faces several questions: how do the Landau coefficients a2k, which depend, besides the control parameter J U, on the scaled chemical potential m U, manage to switch from ‘mean field-like’ to ‘multicritical’ upon variation of m U ? How does one obtain nontrivial critical exponents from this approach, as opposed to the trivial exponent b = 1 2 showing up in equation (5)? What effort would be required to compute these critical exponents along this line with sizeable accuracy? These are the questions we address in the present work, which constitutes a clarification and significant extension of our previous brief communication [17]
The purpose of this section is to investigate the exponents b = b (m U ) which govern the emergence of the order parameter according to ymin ~ (J U - (J U )c)b (m U )
Summary
Commons Attribution 3.0 superfluid transition occurring in the two-dimensional Bose–Hubbard model, and the divergence licence. Exponents of its one- and two-particle correlation functions. This approach correctly reproduces the critical exponent of the threethe work, journal citation dimensional XY universality class. Because divergence exponents can be computed in an efficient and DOI. Manner by hypergeometric analytic continuation, our strategy is applicable to a wide class of systems
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