DMRG for Quantum Spin Systems. Construction of the Reservoirs.

Andreas Weichselbaum, Jan von Delft

Hanggai Nuomin, Jiaxi Wu, Peng Zhang +1 more

It is challenging to simulate open quantum systems that are connected to a reservoir through multiple channels. For example, vibrations may induce fluctuations in both energy gaps and electronic couplings, which represent two independent channels of system-bath couplings. Systems of this kind are ubiquitous in the processes of excited state radiationless decay. Combined with density matrix renormalization group (DMRG) and matrix product states (MPS) methods, we develop an interaction-picture chain mapping strategy for vibrational reservoirs to simulate the dynamics of these open systems, resulting in time-dependent spatially local system-bath couplings in the chain-mapped Hamiltonian. This transformation causes the entanglement generated by the system-bath interactions to be restricted within a narrow frequency window of vibrational modes, enabling efficient DMRG/MPS dynamical simulations. We demonstrate the utility of this approach by simulating singlet fission dynamics using a generalized spin-boson Hamiltonian with both diagonal and off-diagonal system-bath couplings. This approach generalizes an earlier interaction-picture chain mapping scheme, allowing for efficient and exact simulation of systems with multi-channel system-bath couplings using matrix product states, which may further our understanding of nonlocal exciton-phonon couplings in exciton transport and the non-Condon effect in energy and electron transfer.

Hiromi Otsuka, 博巳 大塚

C. A. Büsser

We investigate the entanglement between the spins of two quantum dots that are not connected at once to the same system. Quantum entanglement between localized spins is an essential property for the development of quantum computing and quantum information. It is for this reason that generating and controlling an entangled state between quantum dots received great attention in the later years. In this work, we show that the information on the spin orientation of a quantum dot can be kept, using the Kondo entanglement, in a reservoir of electrons. Then, this information can be transmitted to another dot after the first dot has been uncoupled from the reservoirs. We use a double quantum dot system in a parallel geometry to construct the initial state, where each dot interacts with reservoirs of different symmetries. We chose a phase in the couplings to induce an antiferromagnetic spin correlation between the dots. The time evolution of the initial state has been analyzed using the time-dependent density matrix renormalization group method. We found that a partially entangled state between the dots can be obtained, even if they are not connected at the same time. This entangled state is formed just during the transient and is destroyed in the stationary state. The stability of the state found in the transient is shown. To understand the details of these phenomena, a canonical transformation of the real space is used.

Tao Xiang, Xiaoqun Wang

A. Šurda

A new approach to derivation of various effective-field approximation for lattice spin models is presented. It is shown that it can give a number of methods, including the DMRG method, that can be used to find generally inhomogeneous solutions of 2D classical lattice problems. A method, closely related the DMRG method but without necessity to perform any renormalization, is derived, yielding results practically not different from the DMRG ones. The matrix-product wave function of Rommer and Östlund can be constructed from the output of the method. The computational costs of all the derived methods are smaller than those of the DMRG. Most of the results are applicable to the 1D quantum systems, as well.