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Register a new userAb-initio study of interacting fermions at finite temperature with neural canonical transformation
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We present a variational density matrix approach to the thermal properties of interacting fermions in the continuum. The variational density matrix is parametrized by a permutation equivariant many-body unitary transformation together with a discrete probabilistic model. The unitary transformation is implemented as a quantum counterpart of neural canonical transformation, which incorporates correlation effects via a flow of fermion coordinates. As the first application, we study electrons in a two-dimensional quantum dot with an interaction-induced crossover from Fermi liquid to Wigner molecule. The present approach provides accurate results in the low-temperature regime, where conventional quantum Monte Carlo methods face severe difficulties due to the fermion sign problem. The approach is general and flexible for further extensions, thus holds the promise to deliver new physical results on strongly correlated fermions in the context of ultracold quantum gases, condensed matter, and warm dense matter physics.
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Efficient ab initio calculations of correlated materials at finite temperature require compact representations of the Greens functions both in imaginary time and Matsubara frequency. In this paper, we introduce a general procedure which generates sparse sampling points in time and frequency from compact orthogonal basis representations, such as Chebyshev polynomials and intermediate representation (IR) basis functions. These sampling points accurately resolve the information contained in the Greens function, and efficient transforms between different representations are formulated with minimal loss of information. As a demonstration, we apply the sparse sampling scheme to diagrammatic $GW$ and GF2 calculations of a hydrogen chain, of noble gas atoms and of a silicon crystal.
We present a simple derivation of the Hellmann-Feynman theorem at finite temperature. We illustrate its validity by considering three relevant examples which can be used in quantum mechanics lectures: the one-dimensional harmonic oscillator, the one-dimensional Ising model and the Lipkin model. We show that the Hellmann-Feynman theorem allows one to calculate expectation values of operators that appear in the Hamiltonian. This is particularly useful when the total free-energy is available, but there is not direct access to the thermal average of the operators themselves.
We generalize techniques previously used to compute ground-state properties of one-dimensional noninteracting quantum gases to obtain exact results at finite temperature. We compute the order-n Renyi entanglement entropy to all orders in the fugacity in one, two, and three spatial dimensions. In all spatial dimensions, we provide closed-form expressions for its virial expansion up to next-to-leading order. In all of our results, we find explicit volume scaling in the high-temperature limit.
We develop a formalism for computing the non-linear response of interacting integrable systems. Our results are asymptotically exact in the hydrodynamic limit where perturbing fields vary sufficiently slowly in space and time. We show that spatially resolved nonlinear response distinguishes interacting integrable systems from noninteracting ones, exemplifying this for the Lieb-Liniger gas. We give a prescription for computing finite-temperature Drude weights of arbitrary order, which is in excellent agreement with numerical evaluation of the third-order response of the XXZ spin chain. We identify intrinsically nonperturbative regimes of the nonlinear response of integrable systems.
It is known that entanglement can be converted to work in quantum composite systems. In this paper we consider a quench protocol for two initially independent reservoirs $A$ and $B$ described by the quantum thermal states. For a free fermion model at low temperatures, the von Neumann entropy of each reservoir increases once the reservoirs are coupled. At the moment of decoupling there is an energy transfer to the system in the amount set by the von Neumann entropy accumulated during joint evolution of $A$ and $B$. This energy transfer appears as work produced by the quench to decouple the reservoirs. Once the reservoirs are disconnected, the information about their mutual correlations $-$ von Neumann entropy $-$ is stored in the energy increment of each reservoir. This result provides a possibility of a direct readout of quantum correlations at low temperature.
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