Thermodynamics in the vicinity of a relativistic quantum critical point in2+1dimensions

2013/03/31 by Adam Rançon, A. Rancon, O. Kodio +3
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Geometry #Mathematical physics #Order (exchange) #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum critical point #Quantum mechanics #Quantum phase transition #Quantum, superfluid, helium dynamics #Renormalization group #Scaling #cond-mat.quant-gas

paper · pdf · doi:10.1103/physreve.88.012113

published as Phys. Rev. E 88, 012113 (2013) · v1) 16 pages, 10 figures. v2) Revised version

openalex publication_date 2013/07/15 · arxiv created 2013/07/23 · arxiv updated 2013/07/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We study the thermodynamics of the relativistic quantum O(N) model in two space dimensions. In the vicinity of the zero-temperature quantum critical point (QCP), the pressure can be written in the scaling form P(T)=P(0)+N(T³/c²)F_N(\ensuremathΔ/T), where c is the velocity of the excitations at the QCP and |\ensuremathΔ| a characteristic zero-temperature energy scale. Using both a large-N approach to leading order and the nonperturbative renormalization group, we compute the universal scaling function F_N. For small values of N (N\ensuremath\lesssim10) we find that F_N(x) is nonmonotonic in the quantum critical regime (|x|\ensuremath\lesssim1) with a maximum near x=0. The large-N approach---if properly interpreted---is a good approximation both in the renormalized classical (x\ensuremath\lesssim\ensuremath-1) and quantum disordered (x\ensuremath\gtrsim1) regimes, but fails to describe the nonmonotonic behavior of F_N in the quantum critical regime. We discuss the renormalization-group flows in the various regimes near the QCP and make the connection with the quantum nonlinear sigma model in the renormalized classical regime. We compute the Berezinskii-Kosterlitz-Thouless transition temperature in the quantum O(2) model and find that in the vicinity of the QCP the universal ratio T_BKT/\ensuremathρ_s(0) is very close to \ensuremathπ/2, implying that the stiffness \ensuremathρ_s(T_BKT^\ensuremath-) at the transition is only slightly reduced with respect to the zero-temperature stiffness \ensuremathρ_s(0). Finally, we briefly discuss the experimental determination of the universal function F₂ from the pressure of a Bose gas in an optical lattice near the superfluid--Mott-insulator transition.

Citations

• Theoretical estimates of the critical exponents of the superfluid transition inHe<mml:none/><mml:none/><mml:mprescripts/><mml:none/>4by lattice methods
• Higgs Mode in a Two-Dimensional Superfluid
• From local to critical fluctuations in lattice models: A nonperturbative renormalization-group approach
• Transition from a Strongly Interacting 1D Superfluid to a Mott Insulator
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Exact evolution equation for the effective potential
• Nonperturbative renormalization flow and essential scaling for the Kosterlitz-Thouless transition
• Optimization of the derivative expansion in the nonperturbative renormalization group
• The critical properties of the two-dimensional xy model
• Ordering, metastability and phase transitions in two-dimensional systems
• Kosterlitz-Thouless Phase Transition in the Two Dimensional LinearσModel
• Nonperturbative renormalization-group approach to frustrated magnets