Critical behavior of Tan's contact for bosonic systems with a fixed chemical potential

Abstract

The temperature dependence of Tan's contact parameter $C$ and its derivatives for spin gapped quantum magnets are investigated. We use the paradigm of Bose-Einstein condensation (BEC) to describe the low temperature properties of quasiparticles in the system known as triplons. Since the number of particles and the condensate fraction are not fixed we use the $\mu VT$ ensemble to calculate the thermodynamic quantities. The interactions are treated at the Hartree-Fock-Bogoliubov approximation level. We obtained the temperature dependence of $C$ and its derivative with respect to temperature and applied magnetic field both above and below $T_c$ of the phase transition from the normal phase to BEC. We have shown that $C$ is regular, while its derivatives are discontinuous at $T_c$ in accordance with Ehrenfest's classification of phase transitions. Moreover, we have found a sign change in $\partial C/\partial T$ close to the critical temperature. As to the quantum critical point, $C$ and its derivatives are regular as a function of the control parameter $r$, which induces the quantum phase transition. At very low temperatures, one may evaluate $C$ simply from the expression $C=m^2{\mu }^2/{\bar{a}}^4$, where the only parameter effective mass of quasiparticles should be estimated. We propose a method for measuring of Tan's contact for spin gapped dimerized magnets.

23 pages, 4 captioned figures

References in corpus (21)

• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• Finite Temperature Models of Bose-Einstein Condensation
• Verification of universal relations in a strongly interacting Fermi gas
• Two-dimensional dynamics of expansion of a degenerate Bose gas
• Measurement of the Homogeneous Contact of a Unitary Fermi gas
• Universal Relations for Identical Bosons from 3-Body Physics
• Two and Three-body Contacts in the Unitary Bose Gas
• Bose-Einstein Condensation of Magnons in TlCuCl3: Phase diagram and specific heat from a self-consistent Hartee-Fock calculation with a realistic dispersion relation
• Universal contact for a Tonks-Girardeau gas at finite temperature
• Momentum-resolved observation of thermal and quantum depletion in an interacting Bose gas
• Short-range correlations and entropy in ultracold atomic Fermi gases
• Breakdown of Tan's relation in lossy one-dimensional Bose gases
• Universality in one-dimensional fermions at finite temperature: Density, pressure, compressibility, and contact
• Universal Tan relations for quantum gases in one dimension
• Critical behaviours of contact near phase transitions
• Particle-hole symmetry breaking in a spin-dimer system TlCuCl${}_3$ observed at 100 T
• Tan's two-body contact across the superfluid transition of a planar Bose gas
• The fraction of Bose-Einstein condensed triplons in TlCuCl3 from magnetization M(T,H)-data
• Tan's contact as an indicator of completeness and self-consistency of a theory
• First ESR Detection of Higgs Amplitude Mode and Analysis with Extended Spin-Wave Theory in Dimer System KCuCl${}_3$

Cited by in corpus (4)

• Self-consistent theory of a homogeneous binary Bose mixture with strong repulsive interspecies interaction
• On the anomalous density of a dilute homogeneous Bose gas
• Hugenholtz -- Pines relations and the critical temperature of a Rabi coupled binary Bose system
• Defining a critical temperature of a crossover from BEC to the normal phase in anisotropic quantum magnets