Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session W6: Quantum Information Meets Density Matrix Renormalization |
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Sponsoring Units: DCOMP Chair: Steve White, UCI Room: LACC 502A |
Thursday, March 24, 2005 2:30PM - 3:06PM |
W6.00001: On the simulation of dissipative time-dependent systems Invited Speaker: Recently, a DMRG-based algorithm to simulate Hamiltonian dynamics in one dimensional quantum systems has been proposed [G. Vidal, Phys. Rev. Lett. 93, 040502 (2004)]. I will discus an extension of the algorithm to open system dynamics [M. Zwolak, G. Vidal, Phys. Rev. Lett. 93, 207205 (2004)]. This extension can be used e.g., to compute thermal states or to simulate dissipative dynamics in arbitrary one-dimensional quantum lattices, including systems of bosons and fermions and spin chains. [Preview Abstract] |
Thursday, March 24, 2005 3:06PM - 3:42PM |
W6.00002: On adaptive time-dependent DMRG based on Runge-Kutta methods Invited Speaker: During the past year, the density matrix renormalization group (DMRG) has experienced an unprecedented evolution. Through a convergence with quantum information ideas, it has become a simulation tool that allows one to calculate time-evolution and spectral properties of quantum systems with exceptional accuracy. We present a new real-time evolution DMRG algorithm which works on ladders and systems with interactions beyond nearest neighbors, in contrast to existing Suzuki-Trotter based approaches. We demonstrate its application on several chain and ladder systems. [Preview Abstract] |
Thursday, March 24, 2005 3:42PM - 4:18PM |
W6.00003: On adaptive time-dependent DMRG based on Trotter decompositions Invited Speaker: Ulrich Schollwoeck The integration of concepts from quantum information theory into DMRG has recently allowed the extension of DMRG to high-precision calculations of the time evolution of one-dimensional strongly correlated quantum systems at low algorithmic cost. The key idea is that the reduced Hilbert space of DMRG does not remain static or is extended in time at high algorithmic cost, but adapts itself optimally to the quantum state evolving in time. The adaptation strategy I will present is based on Trotter-decomposing infinitesimal global time-evolutions into local time evolutions that are exact. I want to discuss the potential of this new method presenting an error analysis on the Trotter and DMRG truncation errors in this approach and various applications from magnetism far from equilibrium and ultracold atoms (cf. cond-mat/0403313, 0409692, 0411403) and discuss future areas of application. [Preview Abstract] |
Thursday, March 24, 2005 4:18PM - 4:54PM |
W6.00004: On the link between quantum information theory and DMRG Invited Speaker: The density matrix renormalization group can be formulated as a method that sequentially splits some quantum system into two subsystems and chooses the reduced Hilbert spaces for the subsystems such that the entropy of bipartite entanglement is maximized. This method is optimal for removing the negative effect of a boundary in the performance of real space renormalization groups. An analysis of the growth of bipartite entanglement with system sizes allows one to assess from a quantum information point of view the growth of resources needed to maintain a certain quality of approximation. There emerge interesting links to the geometric entropy of field theories and to quantum information methods for black holes. [Preview Abstract] |
Thursday, March 24, 2005 4:54PM - 5:30PM |
W6.00005: On the matrix product formulation of DMRG and the extension of DMRG to two-dimensional quantum systems Invited Speaker: Matrix product states form the mathematical framework on which both Wilons's numerical renormalization group and White's density matrix renormalization group are build. This insight allows to turn these algorithms into variational methods and to generalize them in various ways. First of all it allows to treat systems with periodic boundary conditions and to calculate ground and excited states with a definite momentum. Secondly, it allows to extend DMRG to systems with finite temperature, and to devise a variational algorithm for doing real time-evolution and for calculating Green's functions. Most notably, we managed to extend the notion of matrix product states to projected entangled pair states for higher dimensional systems. This led to the creation of a variational algorithm to describe ground states and simulate real-time evolution of spin systems in two and higher dimensions. [Preview Abstract] |
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