Related papers: Criticality in Two-Dimensional Quantum Systems: Te…
The entanglement entropy of a pure quantum state of a bipartite system $A \cup B$ is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. Critical ground states of local…
We construct a general wave function with the topological order by introducing the $\mathbb{Z}_{2}$ gauge degrees of freedom, characterizing both the toric code state and double semion state. Via calculating the correlation length defined…
The variational tensor network renormalization approach to two-dimensional (2D) quantum systems at finite temperature is applied for the first time to a model suffering the notorious quantum Monte Carlo sign problem --- the orbital $e_g$…
This thesis is divided into two mainly independent parts: In the first part, we derive a criterion to determine when a translationally invariant Matrix Product State (MPS) has long range localizable entanglement, which indicates that the…
Due to the presence of strong correlations, theoretical or experimental investigations of quantum many-body systems belong to the most challenging tasks in modern physics. Stimulated by tensor networks, we propose a scheme of constructing…
Efficient methods to access the entanglement of a quantum many-body state, where the complexity generally scales exponentially with the system size $N$, have long a concern. Here we propose the Schmidt tensor network state (Schmidt TNS)…
Characterizing complexity and criticality in quantum systems requires diagnostics that are both computationally tractable and physically insightful. We apply a measure of quantum state complexity for n-qubit systems, defined as the…
Topological order in a 2d quantum matter can be determined by the topological contribution to the entanglement R\'enyi entropies. However, when close to a quantum phase transition, its calculation becomes cumbersome. Here we show how…
Strongly correlated layered 2D systems are of central importance in condensed matter physics, but their numerical study is very challenging. Motivated by the enormous successes of tensor networks for 1D and 2D systems, we develop an…
Efficient preparation of many-body ground states is key to harnessing the power of quantum computers in studying quantum many-body systems. In this work, we propose a simple method to design exact linear-depth parameterized quantum circuits…
A classification of SU(2)-invariant Projected Entangled Paired States (PEPS) on the square lattice, based on a unique site tensor, has been recently introduced by Mambrini et al.~\cite{Mambrini2016}. It is not clear whether such…
We introduce a novel tensor network structure augmenting the well-established Tree Tensor Network representation of a quantum many-body wave function. The new structure satisfies the area law in high dimensions remaining efficiently…
Understanding dissipation in 2D quantum many-body systems is a remarkably difficult open challenge. Here we show how numerical simulations for this problem are possible by means of a tensor network algorithm that approximates steady-states…
Quantum phase transitions are a ubiquitous many-body phenomenon that occurs in a wide range of physical systems, including superconductors, quantum spin liquids, and topological materials. However, investigations of quantum critical systems…
Many-body systems when continuous phase transition occurs are mainly built in the interrelationship between particles, implemented through many-body correlations. Some of them may exhibit so-called topological order hardly measured by…
We introduce a class of states of a composite quantum system, the so-called cross states, that turn out to play a major role in the theory of entanglement for a genuinely infinite-dimensional bipartite system. In the case where at least one…
One of the key ingredients of many LOCC protocols in quantum information is a multiparticle (locally) maximally entangled quantum state, aka a critical state, that possesses local symmetries. We show how to design critical states with…
The two-dimensional (2D) random-bond Ising model has a novel multicritical point on the ferromagnetic to paramagnetic phase boundary. This random phase transition is one of the simplest examples of a 2D critical point occurring at both…
We show, via explicit computation on a constrained bosonic model, that the presence of subsystem symmetries can lead to a quantum phase transition (QPT) where the critical point exhibits an emergent enhanced symmetry. Such a transition…
Although quantum mechanics underpins the microscopic behavior of all materials, its effects are often obscured at the macroscopic level by thermal fluctuations. A notable exception is a zero-temperature phase transition, where scaling laws…