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We revisit the problem of the calculation of zero-temperature properties for the dilute two-dimensional Bose gas. By using Popov's hydrodynamic approach and perturbation theory on the two-loop level, we recover not only the known expansion for the ground-state energy but also calculate for the first time the condensate density and Tan's contact. [ABSTRACT FROM AUTHOR]

We investigate the non-equilibrium properties of a weakly interacting Bose gas subjected to a multi-pulsed quench at zero temperature, where the interaction parameter in the Hamiltonian system switches between values and for multiple times. The one-body and two-body correlation functions as well as Tan's contact are calculated. The quench induced excitations are shown to increase with the number of quenches for both and . This implies the possibility to use multi-pulsed quantum quench as a more powerful way as compared to the 'one-off' quench in controllable explorations of non-equilibrium quantum many-body systems. In addition, we study the ultra-short-range property of the two-body correlation function after multiple interaction quenches, which can serve as a probe of the 'Tan's contact' in the experiments. Our findings allow for an experimental probe using state of the art techniques with ultracold quantum gases. [ABSTRACT FROM AUTHOR]

A one-dimensional world is very unusual as there is an interplay between quantum statistics and geometry, and a strong short-range repulsion between atoms mimics Fermi exclusion principle, fermionizing the system. Instead, a system with a large number of components with a single atom in each, on the opposite acquires many bosonic properties. We study the ground-state properties of a multicomponent repulsive Fermi gas trapped in a harmonic trap by a fixed-node diffusion Monte Carlo method. The interaction between all components is considered to be the same. We investigate how the energetic properties (energy, contact) and correlation functions (density profile and momentum distribution) evolve as the number of components is changed. It is shown that the system fermionizes in the limit of strong interactions. Analytical expressions are derived in the limit of weak interactions within the local density approximation for an arbitrary number of components and for one plus one particle using an exact solution.

A system of two-species, one-dimensional fermions, with an attractive two-body interaction of the derivative-delta type, features a scale anomaly. In contrast to the well-known two-dimensional case with contact interactions, and its one-dimensional cousin with three-body interactions (studied recently by some of us and others), the present case displays dimensional transmutation featuring a power-law rather than a logarithmic behavior. We use both the Schrödinger equation and quantum field theory to study bound and scattering states, showing consistency between both approaches. We show that the expressions for the reflection (R) and the transmission (T) coefficients of the renormalized, anomalous derivative-delta potential are identical to those of the regular delta potential. The second-order virial coefficient is calculated analytically using the Beth–Uhlenbeck formula, and we make comments about the proper ϵ B → 0 (where ϵ B is the bound-state energy) limit. We show the impact of the quantum anomaly (which appears as the binding energy of the two-body problem, or equivalently as Tan's contact) on the equation of state and on other universal relations. Our emphasis throughout is on the conceptual and structural aspects of this problem. • The 1D derivative-delta two-body potential provides a model for a fermion gas. • The derivative-delta interaction has a classical SO(2,1) conformal symmetry. • The scale symmetry breaks as a quantum anomaly, with dimensional transmutation. • The scale anomaly generates a bound state and non-trivial, anomalous scattering. • The anomaly, driven by Tan's contact, gives an equation of state and virial relations. [ABSTRACT FROM AUTHOR]

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 μVT 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 ∂ C /∂ T close to the critical temperature. As to the quantum critical point, C simply from the expressionC=m2μ2/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.r , which induces the quantum phase transition. At very low temperatures, one may evaluate C simply from the expressionC=m2μ2/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., (© 2021 IOP Publishing Ltd.)