Related papers: Matrix Product State and Quantum Phase Transitions…
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…
This paper introduces a Heisenberg picture approach to Matrix Product States (MPS), offering a rigorous yet intuitive framework to explore their structure and classification. MPS efficiently represent ground states of quantum many-body…
First order quantum phase transitions (1QPTs) are signaled, in the thermodynamic limit, by discontinuous changes in the ground state properties. These discontinuities affect expectation values of observables, including spatial correlations.…
Quantum turbulence spans length scales from the system size $L$ to the healing length $\xi$, making direct numerical simulations (DNS) of the Gross-Pitaevskii (GP) equation computationally expensive when $L \gg \xi$. We present a matrix…
The ground-state phase diagram and quantum phase transitions (QPTs) in a spin-1 compass chain are investigated by the infinite time-evolving block decimation (iTEBD) method. Various phases are discerned by energy densities, spin…
The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study 1+1 dimensional one flavour…
Tensor network states are used extensively as a mathematically convenient description of physically relevant states of many-body quantum systems. Those built on regular lattices, i.e. matrix product states (MPS) in dimension 1 and projected…
I first give an overview of the thesis and Matrix Product States (MPS) representation of quantum spin chains with an improvement on the conventional notation. The rest of this thesis is divided into two parts. The first part is devoted to…
Many fractional quantum Hall states can be expressed as a correlator of a given conformal field theory used to describe their edge physics. As a consequence, these states admit an economical representation as an exact Matrix Product States…
Using extensive numerical analysis of 20,000 randomly generated two-qubit states, we provide a quantitative analysis of the connection between entanglement measures and Maximized Quantum Fisher Information (MQFI). Our systematic study shows…
There has been a problem of gauge ambiguities with the Rabi Hamiltonian due to the fact that it can be derived from two formally different but physically equivalent fundamental Hamiltonians. This problem has recently been resolved for…
We consider the square lattice $S$=1/2 quantum compass model (QCM) parameterized by $J_x, J_z$, under a field, $\mathbf{h}$, in the $x$-$z$ plane. At the special field value, $(h_x^\star,h_z^\star)$=$2S(J_x,J_z)$, we show that the QCM…
Quantum phase transitions and observables of interest of the ground state in the Tavis-Cummings model are analyzed, for any number of atoms, by using a tensorial product of coherent states. It is found that this "trial" state constitutes a…
The determination of ground state properties of quantum systems is a fundamental problem in physics and chemistry, and is considered a key application of quantum computers. A common approach is to prepare a trial ground state on the quantum…
Quantum computing is finding promising applications in optimization, machine learning and physics, leading to the development of various models for representing quantum information. Because these representations are often studied in…
We investigate two variants of quantum compass models (QCMs). The first, an orbital-only honeycomb QCM, is shown to exhibit a quantum phase transition (QPT) from a $XX$- to $ZZ$-ordered phase in the $3d$-Ising universality class, in accord…
Our study employs a connected correlation matrix to quantify Quantum Entanglement. The matrix encompasses all necessary measures for assessing the degree of entanglement between particles. We begin with a three-qubit state and involve…
Quantum many body physics simulations with Matrix Product States can often be accelerated if the quantum symmetries present in the system are explicitly taken into account. Conventionally, quantum symmetries have to be determined before…
We show that general string-net condensed states have a natural representation in terms of tensor product states (TPS) . These TPS's are built from local tensors. They can describe both states with short-range entanglement (such as the…
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…