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We investigate the relation between static correlation functions in the ground state of local quantum many-body Hamiltonians and the dispersion relations of the corresponding low energy excitations using the formalism of tensor network…

Matrix product states play an important role in quantum information theory to represent states of many-body systems. They can be seen as low-dimensional subvarieties of a high-dimensional tensor space. In these notes, we consider two…

Representation Theory · Mathematics 2023-12-05 Tim Seynnaeve

This paper introduces matrix product state (MPS) decomposition as a new and systematic method to compress multidimensional data represented by higher-order tensors. It solves two major bottlenecks in tensor compression: computation and…

Machine Learning · Statistics 2017-08-02 Johann A. Bengua , Ho N. Phien , Hoang D. Tuan , Minh N. Do

We study the tractability of classically simulating critical phenomena in the quench dynamics of one-dimensional transverse field Ising models (TFIMs) using highly truncated matrix product states (MPS). We focus on two paradigmatic…

Improving the understanding of strongly correlated quantum many body systems such as gases of interacting atoms or electrons is one of the most important challenges in modern condensed matter physics, materials research and chemistry.…

Quantum Physics · Physics 2015-12-18 C. Eichler , J. Mlynek , J. Butscher , P. Kurpiers , K. Hammerer , T. J. Osborne , A. Wallraff

The canonical form of Matrix Product States (MPS) and the associated fundamental theorem, which relates different MPS representations of a state, are the theoretical framework underlying many of the analytical results derived through MPS,…

Quantum Physics · Physics 2018-04-17 Gemma De las Cuevas , J. Ignacio Cirac , Norbert Schuch , David Perez-Garcia

Matrix Product States (MPS) are used for the simulation of the real-time dynamics induced by an electric quench on the vacuum state of the massive Schwinger model. For small quenches it is found that the obtained oscillatory behavior of…

High Energy Physics - Lattice · Physics 2017-12-06 Boye Buyens , Jutho Haegeman , Florian Hebenstreit , Frank Verstraete , Karel Van Acoleyen

Tensor network states, especially Matrix Product States (MPS), are crucial tools for studying how particles in large quantum systems are entangled with each other. MPS are particularly effective for modeling systems in one-dimensional…

High Energy Physics - Theory · Physics 2025-02-03 Niloofar Vardian

We have developed a new approach based on matrix product representations of ground states to study Quantum Phase Transitions (QPT). As confirmation of the power of our approach we have analytically analyzed the XXZ spin-one chain with…

Quantum Physics · Physics 2009-09-17 K. Heshami , S. Raeisi

This work presents a method for studying low-energy physics in highly correlated magnetic systems using the matrix product state (MPS) manifold. We adapt the spin-wave approach, which has been very successful in modeling certain…

Quantum Physics · Physics 2024-10-31 Sebastian Leontica , Andrew G. Green

Matrix Product States can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system. We introduce a new family of states which extends this definition to two dimensions. Like in Matrix Product…

Matrix product states, a key ingredient of numerical algorithms widely employed in the simulation of quantum spin chains, provide an intriguing tool for quantum phase transition engineering. At critical values of the control parameters on…

Statistical Mechanics · Physics 2009-11-11 M. Cozzini , R. Ionicioiu , P. Zanardi

A way of constructing continuous matrix product states (cMPS) for coupled fields is presented here. The cMPS is a variational \emph{ansatz} for the ground state of quantum field theories in one dimension. Our proposed scheme is based in the…

Quantum Physics · Physics 2017-01-19 Fernando Quijandría , Juan José García-Ripoll , David Zueco

In this note, we describe a method for reconstructing matrix product states from a small number of efficiently-implementable measurements. Our method is exponentially faster than standard tomography, and it can also be used to certify that…

Quantum Physics · Physics 2010-02-26 Olivier Landon-Cardinal , Yi-Kai Liu , David Poulin

For quantum many-body systems in one dimension, computational complexity theory reveals that the evaluation of ground-state energy remains elusive on quantum computers, contrasting the existence of a classical algorithm for temperatures…

Statistical Mechanics · Physics 2024-06-11 Atsushi Iwaki , Chisa Hotta

Identification of the optimal quantum metrological protocols in realistic many particle quantum models is in general a challenge that cannot be efficiently addressed by the state-of-the-art numerical and analytical methods. Here we provide…

The density-matrix renormalization group method has become a standard computational approach to the low-energy physics as well as dynamics of low-dimensional quantum systems. In this paper, we present a new set of applications, available as…

We quantify how well matrix product states approximate exact ground states of 1-D quantum spin systems as a function of the number of spins and the entropy of blocks of spins. We also investigate the convex set of local reduced density…

Strongly Correlated Electrons · Physics 2007-05-23 F. Verstraete , J. I. Cirac

The tensor product representation of quantum states leads to a promising variational approach to study quantum phase and quantum phase transitions, especially topological ordered phases which are impossible to handle with conventional…

Strongly Correlated Electrons · Physics 2013-05-29 Xie Chen , Bei Zeng , Zheng-Cheng Gu , Isaac L. Chuang , Xiao-Gang Wen

Quantum many-body scarred systems host nonthermal excited eigenstates immersed in a sea of thermal ones. In cases where exact expressions for these special eigenstates are not known, it is computationally demanding to distinguish them from…

Strongly Correlated Electrons · Physics 2023-07-13 Shun-Yao Zhang , Dong Yuan , Thomas Iadecola , Shenglong Xu , Dong-Ling Deng