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Register a new userGr{u}neisen Parameters: origin, identity and quantum refrigeration
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In solid state physics, the Gr{u}neisen parameter (GP), originally introduced in the study of the effect of changing the volume of a crystal lattice on its vibrational frequency, has been widely used to investigate the characteristic energy scales of systems with respect to the changes of external potentials. On the other hand, the GP is little investigated in a strongly interacting quantum gas systems. Here we report on our general results on the origin of GP, new identity and caloric effects in quantum gases of ultracold atoms. We prove that the symmetry of the dilute quantum gas systems leads to a simple identity among three different types of GPs, quantifying caloric effect induced respectively by variations of volume, magnetic field and interaction. Using exact Bethe ansatz solutions, we present a rigorous study of these different GPs and the quantum refrigeration in one-dimensional Bose and Femi gases. Based on the exact equations of states of these systems, we obtain analytic results for the singular behaviour of the GPs and the caloric effects at quantum criticality. We also predict the existence of the lowest temperature for cooling near a quantum phase transition. It turns out that the interaction ramp-up and -down in quantum gases provides a promising protocol of quantum refrigeration in addition to the usual adiabatic demagnetization cooling in solid state materials.
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Using Hartree-Fock-Bogoliubov (HFB) approach we obtained analytical expressions for thermodynamic quantities of the system of triplons in spin gapped quantum magnets such as magnetization, heat capacity and the magnetic Gr{u}neisen parameter $Gamma_H$. Near the critical temperature, $Gamma_H$ is discontinuous and changes its sign upon the Bose-Einstein condensation (BEC) of triplons. On the other hand, in the widely used Hartree-Fock-Popov (HFP) approach there is no discontinuity neither in the heat capacity nor in the Gr{u}neisen parameter. We predict that in the low-temperature limit and near the critical magnetic field $H_c$, $Gamma_H$ diverges as $Gamma_Hsim 1/T^{2}$, while it scales as $Gamma_Hsim 1/(H-H_c)$ as the magnetic field approaches the quantum critical point at $H_c$.
Complete expressions of the thermal-expansion coefficient $alpha$ and the Gr{u}neisen parameter $Gamma$ are derived on the basis of the self-consistent renormalization (SCR) theory. By considering zero-point as well as thermal spin fluctuation under the stationary condition, the specific heat for each class of the magnetic quantum critical point (QCP) specified by the dynamical exponent $z=3$ (FM) and $z=2$ (AFM) and the spatial dimension ($d=3$ and $2$) is shown to be expressed as $C_{V}=C_a-C_b$, where $C_a$ is dominant at low temperatures, reproducing the past SCR criticality endorsed by the renormalization group theory. Starting from the explicit form of the entropy and using the Maxwell relation, $alpha=alpha_a+alpha_b$ (with $alpha_a$ and $alpha_b$ being related to $C_a$ and $C_b$, respectively) is derived, which is proven to be equivalent to $alpha$ derived from the free energy. The temperature-dependent coefficient found to exist in $alpha_b$, which is dominant at low temperatures, contributes to the crossover from the quantum-critical regime to the Curie-Weiss regime and even affects the quantum criticality at 2d AFM QCP. Based on these correctly calculated $C_{V}$ and $alpha$, Gr{u}neisen parameter $Gamma=Gamma_a+Gamma_b$ is derived, where $Gamma_a$ and $Gamma_b$ contain $alpha_a$ and $alpha_b$, respectively. The inverse susceptibility coupled to the volume $V$ in $Gamma_b$ gives rise to divergence of $Gamma$ at the QCP for each class even though characteristic energy scale of spin fluctuation $T_0$ is finite at the QCP, which gives a finite contribution in $Gamma_a=-frac{V}{T_0}left(frac{partial T_0}{partial V}right)_{T=0}$. General properties of $alpha$ and $Gamma$ including their signs as well as the relation to $T_0$ and the Kondo temperature in temperature-pressure phase diagrams of Ce- and Yb-based heavy electron systems are discussed.
The mechanism of not diverging Gr{u}neisen parameter in the quantum critical heavy-fermion quasicrystal (QC) Yb$_{15}$Al$_{34}$Au$_{51}$ is analyzed. We construct the formalism for calculating the specific heat $C_V(T)$, the thermal-expansion coefficient $alpha(T)$, and the Gr{u}neisen parameter $Gamma(T)$ near the quantum critical point of the Yb valence transition. By applying the framework to the QC, we calculate $C_V(T)$, $alpha(T)$, and $Gamma(T)$, which explains the measurements. Not diverging $Gamma(T)$ is attributed to the robustness of the quantum criticality in the QC under pressure. The difference in $Gamma(T)$ at the lowest temperature between the QC and approximant crystal is shown to reflect the difference in the volume derivative of characteristic energy scales of the critical Yb-valence fluctuation and the Kondo temperature. Possible implications of our theory to future experiments are also discussed.
In this study, the temperature dependence of elastic constants $C_{11}$, $C_{33}$, $C_{rm E} = (C_{11}-C_{12})/2$, $C_{66}$ and $C_{44}$ of the iron-based superconductor Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ (0 $leqq x leqq$ 0.245) have been measured. This system shows a large elastic softening in $C_{66}$ towards low temperatures. In addition to $C_{66}$, which originates from orthorhombic structural fluctuation, the samples near the optimal concentration show remarkable structural fluctuation in $C_{11}$ and $C_{33}$ elastic modes, which correspond to $Gamma_{1}$ (C4) symmetry. It suggests the existence of diverse fluctuations in this system. Gr{ u}neisen parameters were analyzed under some assumptions for structural and magnetic transition temperatures. Results showed that the Gr{ u}neisen parameters for the inter-plane strain are remarkably enhanced toward the QCP, while those for the in-plane stress tend to turn down near the QCP. Gr{ u}neisen parameters for the superconducting transition are anisotropic and shows remarkable Co-concentration dependence, suggesting that the in-plane isotropic compression and inter-layer elongation enhance the superconductivity. The correlation of Gr{ u}neisen parameters between $T_{rm S}$, $T_{rm N}$ and $T_{rm sc}$ shows $c$-axis elongation and its relevant role in the emergence of superconductivity in this system.
Using ultracold alkaline-earth atoms in optical lattices, we construct a quantum simulator for U(N) and SU(N) lattice gauge theories with fermionic matter based on quantum link models. These systems share qualitative features with QCD, including chiral symmetry breaking and restoration at non-zero temperature or baryon density. Unlike classical simulations, a quantum simulator does not suffer from sign problems and can address the corresponding chiral dynamics in real time.
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