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Many topologically nontrivial states of matter possess gapless degrees of freedom on the boundary, and when these boundary states delocalize into the bulk, a phase transition occurs and the system becomes topologically trivial. We show that…
The simulation of out-of-equilibrium dissipative quantum many body systems is a problem of fundamental interest to a number of fields in physics, ranging from condensed matter to cosmology. For unitary systems, tensor network methods have…
We study the scaling behavior of the entanglement entropy of two dimensional conformal quantum critical systems, i.e. systems with scale invariant wave functions. They include two-dimensional generalized quantum dimer models on bipartite…
Tensor-network methods are used to perform a comparative study of the two-dimensional classical Heisenberg and $\mathrm{RP}^2$ models. We demonstrate that uniform matrix product states (MPS) with explicit $\mathrm{SO}(3)$ symmetry can probe…
A considerable success in phenomenological description of high-T$_{\rm c}$ superconductors has been achieved within the paradigm of Quantum Critical Point (QCP) - a parental state of a variety of exotic phases that is characterized by dense…
We study the bipartite entanglement entropy of the two-dimensional (2D) transverse-field Ising model in the thermodynamic limit using series expansion methods. Expansions are developed for the Renyi entropy around both the small-field and…
In this paper we study the ground state properties of a ladder Hamiltonian with chiral $SU(2)$-invariant spin interactions, a possible first step towards the construction of truly two dimensional non-trivial systems with chiral properties…
Tensor network techniques are becoming increasingly popular tools to solve partial differential equations within the so-called quantics representation. Their popularity stems from the fact that their spatial resolution depends only…
The critical theories for the topological phase transitions of integer quantum Hall states to a trivial insulating state with the same symmetry can be obtained by calculating the ground state entanglement spectrum under a symmetric…
The outcomes of projective measurements on a quantum many-body system in a chosen basis are inherently probabilistic. The Shannon entropy of this probability distribution (the "diagonal entropy") often reveals universal features, such as…
Within the framework of imaginary-time evolution for matrix product states, we introduce a cluster version of the infinite time-evolving block decimation algorithm for simulating quantum many-body systems, addressing the computational…
In recent years considerable progress has been made towards developing a general theory of quantum entanglement. In particular, criteria to decide whether a given quantum state is entangled are of high theoretical and practical interest.…
We analyse the entanglement structure of states generated by random constant-depth two-dimensional quantum circuits, followed by projective measurements of a subset of sites. By deriving a rigorous lower bound on the average entanglement…
An efficient algorithm is developed for quantum spin tubes in the context of the tensor network representations. It allows to efficiently compute the ground-state fidelity per lattice site, which in turn enables us to identify quantum…
The ability to selectively measure, initialize, and reuse qubits during a quantum circuit enables a mapping of the spatial structure of certain tensor-network states onto the dynamics of quantum circuits, thereby achieving dramatic resource…
We consider the two-dimensional topological Chern insulator in the presence of static disorder. Generic quantum states in this system are Anderson localized. However, topology requires the presence of a subset of critical states, with…
The study of low-dimensional quantum systems has proven to be a particularly fertile field for discovering novel types of quantum matter. When studied numerically, low-energy states of low-dimensional quantum systems are often approximated…
We show how to formulate a lattice gauge theory whose naive continuum limit corresponds to two-dimensional (Euclidean) quantum gravity including a positive cosmological constant. More precisely the resultant continuum theory corresponds to…
Matrix product states (MPS) illustrate the suitability of tensor networks for the description of interacting many-body systems: ground states of gapped $1$-D systems are approximable by MPS as shown by Hastings [J. Stat. Mech. Theor. Exp.,…
We characterize the variational power of quantum circuit tensor networks in the representation of physical many-body ground-states. Such tensor networks are formed by replacing the dense block unitaries and isometries in standard tensor…