scholarly journals Simulating local measurements on a quantum many-body system with stochastic matrix product states

2010 ◽  
Vol 81 (1) ◽  
Author(s):  
Søren Gammelmark ◽  
Klaus Mølmer
Keyword(s):  
Stochastic Matrix ◽  
Matrix Product ◽  
Body System ◽  
Many Body ◽  
Matrix Product States ◽  
Local Measurements

scholarly journals Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 984
Author(s):  
Regina Finsterhölzl ◽  
Manuel Katzer ◽  
Andreas Knorr ◽  
Alexander Carmele
Keyword(s):  
Time Evolution ◽  
Nearest Neighbor ◽  
Matrix Product ◽  
Body System ◽  
Many Body ◽  
Initial State ◽  
Matrix Product States ◽  
Open Quantum ◽  
Many Body Systems ◽  
The Many

This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of N=30.

scholarly journals Stochastic Matrix Product States

2010 ◽  
Vol 104 (21) ◽  
Author(s):  
Kristan Temme ◽  
Frank Verstraete
Keyword(s):  
Stochastic Matrix ◽  
Matrix Product ◽  
Matrix Product States

scholarly journals Chebyshev Matrix Product States with Canonical Orthogonalization for Spectral Functions of Many-Body Systems

2021 ◽  
Author(s):  
Tong Jiang ◽  
Jiajun Ren ◽  
Zhigang Shuai
Keyword(s):  
Ab Initio ◽  
Excited States ◽  
Time Dependent ◽  
Matrix Product ◽  
Effective Hamiltonian ◽  
Many Body ◽  
Spectral Functions ◽  
Matrix Product States ◽  
Many Body Systems ◽  
First Time

We propose a method to calculate the spectral functions of many-body systems by Chebyshev expansion in the framework of matrix product states coupled with canonical orthogonalization (coCheMPS). The canonical orthogonalization can improve the accuracy and efficiency significantly because the orthogonalized Chebyshev vectors can provide an ideal basis for constructing the effective Hamiltonian in which the exact recurrence relation can be retained. In addition, not only the spectral function but also the excited states and eigen energies can be directly calculated, which is usually impossible for other MPS-based methods such as time-dependent formalism or correction vector. The remarkable accuracy and efficiency of coCheMPS over other methods are demonstrated by calculating the spectral functions of spin chain and ab initio hydrogen chain. For the first time we demonstrate that Chebyshev MPS can be used to deal with ab initio electronic Hamiltonian effectively. We emphasize the strength of coCheMPS to calculate the low excited states of systems with sparse discrete spectrum. We also caution the application for electron-phonon systems with dense density of states.

scholarly journals Logarithmic growth of local entropy and total correlations in many-body localized dynamics

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 250
Author(s):  
Fabio Anza ◽  
Francesca Pietracaprina ◽  
John Goold
Keyword(s):  
Anderson Localization ◽  
Conserved Quantities ◽  
Body System ◽  
Local Entropy ◽  
Many Body ◽  
Local Measurements ◽  
Non Local ◽  
Experimental Technology ◽  
Unbiased Basis ◽  
Logarithmic Growth

The characterizing feature of a many-body localized phase is the existence of an extensive set of quasi-local conserved quantities with an exponentially localized support. This structure endows the system with the signature logarithmic in time entanglement growth between spatial partitions. This feature differentiates the phase from Anderson localization, in a non-interacting model. Experimentally measuring the entanglement between large partitions of an interacting many-body system requires highly non-local measurements which are currently beyond the reach of experimental technology. In this work we demonstrate that the defining structure of many-body localization can be detected by the dynamics of a simple quantity from quantum information known as the total correlations which is connected to the local entropies. Central to our finding is the necessity to propagate specific initial states, drawn from the Hamiltonian unbiased basis (HUB). The dynamics of the local entropies and total correlations requires only local measurements in space and therefore is potentially experimentally accessible in a range of platforms.

scholarly journals Quantum Gross-Pitaevskii Equation

2017 ◽  
Vol 3 (1) ◽  
Author(s):  
Jutho Haegeman ◽  
Damian Draxler ◽  
Vid Stojevic ◽  
Ignacio Cirac ◽  
Tobias Osborne ◽  
...  
Keyword(s):  
Mean Field ◽  
Pitaevskii Equation ◽  
Matrix Product ◽  
Steady State Response ◽  
Body System ◽  
Many Body ◽  
One Dimensional ◽  
State Response ◽  
Quantum Liquids ◽  
Full Quantum

We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational manifold of continuous matrix product states. This allows for a full quantum description of many body system —including entanglement and correlations— and thus extends significantly beyond the usual mean-field description of the Gross-Pitaevskii equation, which is known to fail for (quasi) one-dimensional systems. By linearizing around a stationary solution, we furthermore derive an associated generalization of the Bogoliubov – de Gennes equations. This framework is applied to compute the steady state response amplitude to a periodic perturbation of the potential.

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