Continuous matrix product density operators for quantum fields at finite temperature

Hendrickje Nadeau

Frank Verstraete, Juan José García‐Ripoll, J. I. Cirac

We show how to simulate numerically the evolution of 1D quantum systems under dissipation as well as in thermal equilibrium. The method applies to both finite and inhomogeneous systems, and it is based on two ideas: (a) a representation for density operators which extends that of matrix product states to mixed states; (b) an algorithm to approximate the evolution (in real or imaginary time) of matrix product states which is variational.

Alexander C. Tiegel, Salvatore R. Manmana, Thomas Pruschke +1 more

We present a flexible density-matrix renormalization group approach to calculate finite-temperature spectral functions of one-dimensional strongly correlated quantum systems. The method combines the purification of the finite-temperature density operator with a moment expansion of the Green's function. Using this approach, we study finite-temperature properties of dynamical spectral functions of spin-$1/2$ XXZ chains with Dzyaloshinskii-Moriya interactions in magnetic fields and analyze the effect of these symmetry breaking interactions on the nature of the finite-temperature dynamic spin structure factor.

Alfred Wehrl

Erickson Tjoa, J. Ignacio Cirac

In this work we introduce an ansatz for continuous matrix product operators for quantum field theory. We show that (i) they admit a closed-form expression in terms of finite number of matrix-valued functions without reference to any lattice parameter; (ii) they are obtained as a suitable continuum limit of matrix product operators; (iii) they preserve the entanglement area law directly in the continuum, and in particular they map continuous matrix product states (cMPS) to another cMPS. As an application, we use this ansatz to construct several families of continuous matrix product unitaries beyond quantum cellular automata.

Atsushi Iwaki, Shimizu Akira, Chisa Hotta