A Non-Perturbative Renormalization Group approach to quantum XY spin models

Abstract

We present a Lattice Non-Perturbative Renormalization Group (NPRG) approach to quantum XY spin models by using a mapping onto hardcore bosons. The NPRG takes as initial condition of the renormalization group flow the (local) limit of decoupled sites, allowing us to take into account the hardcore constraint exactly. The initial condition of the flow is equivalent to the large $S$ classical results of the corresponding spin system. Furthermore, the hardcore constraint is conserved along the RG flow, and we can describe both local and long-distance fluctuations in a non-trivial way. We discuss a simple approximation scheme, and solve the corresponding flow equations. We compute both the zero-temperature thermodynamics and the finite temperature phase diagram on the square and cubic lattices. The NPRG allows us to recover the correct critical physics at finite temperature in two and three dimensions. The results compare well with numerical simulations.

v1) 15 pages, 7 figures; v2) typos corrected, references added, published version; v3) typo corrected, new calculation in appendix D, not published in the PRB version; v4) typos corrected, one reference added; v5) correction figure 4; v6) typo corrected in the formula for the s-wave scattering length

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Cited by in corpus (21)

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• Exact renormalization group for quantum spin systems
• Spin functional renormalization group for quantum Heisenberg ferromagnets: Magnetization and magnon damping in two dimensions
• Thermodynamics of the two-dimensional XY model from functional renormalization
• Dissipative spin dynamics in hot quantum paramagnets
• Zero-magnon sound in quantum Heisenberg ferromagnets
• Kosterlitz-Thouless signatures in the low-temperature phase of layered three-dimensional systems
• A rich man's derivation of scaling laws for the Kondo model
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• Comment on "Universal and Non-Universal Correction Terms of Bose Gases in Dilute Region: A Quantum Monte Carlo Study'' [J. Phys. Soc. Jpn. 91, 024001 (2022)]
• Strong-coupling RPA theory of a Bose gas near the superfluid--Mott-insulator transition: universal thermodynamics and two-body contact
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• Constraint effective action and critical correlation functions at fixed magnetization
• Spin functional renormalization group for dimerized quantum spin systems
• Exact generating function of a zero-dimensional supersymmetric non-linear sigma model