Finite-temperature density matrix embedding theory

Abstract

We describe a formulation of the density matrix embedding theory at finite temperature. We present a generalization of the ground-state bath orbital construction that embeds a mean-field finite-temperature density matrix up to a given order in the Hamiltonian, or the Hamiltonian up to a given order in the density matrix. We assess the performance of the finite-temperature density matrix embedding on the 1D Hubbard model both at half-filling and away from it, and the 2D Hubbard model at half-filling, comparing to exact data where available, as well as results from finite-temperature density matrix renormalization group, dynamical mean-field theory, and dynamical cluster approximations. The accuracy of finite-temperature density matrix embedding appears comparable to that of the ground-state theory, with at most a modest increase in bath size, and competitive with that of cluster dynamical mean-field theory.

Toward Practical Quantum Embedding Simulation of Realistic Chemical Systems on Near-term Quantum Computers

“…Along this line, several hybrid methods have been proposed by exploiting different classical methods [31][32][33], such as density matrix embedding theory [34][35][36][37], dynamical mean field theory [38][39][40], tensor network [23,41], and perturbation theory [42]. Density matrix embedding is one of the representative embedding methods that have been theoretically and experimentally developed in several works [6,[34][35][36][37][43][44][45][46][47][48][49][50], yet the practical realization toward realistic chemical systems remains a significant technical challenge.…”

Approximations based on density-matrix embedding theory for density-functional theories

“…Furthermore, different extensions of DMET have been developed to apply the method to time-dependent systems [14] and excited states [34], and to coupled electron-phonon models [29,30]. Also, finite-temperature systems have already been treated with DMET [31]. Numerical shortcomings of the DMET method can be improved by semi-definite programming [39], projected DMET [38] and multiconfigurational DMET [9].…”

On the pure state $v$-representability of density matrix embedding theory

“…Density matrix embedding theory (DMET) [1][2][3][4][5][6][7][8] is a quantum embedding theory designed to treat strong correlation effects in large quantum systems. DMET and its related variants have been successfully applied to a wide range of systems such as Hubbard models 1,4,[9][10][11][12][13][14][15] , quantum spin models [16][17][18] , and a number of strongly correlated molecular and periodic systems 2,5,8,[19][20][21][22][23][24][25][26][27][28][29] .…”