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We consider the repulsive Hubbard model on a class of lattices or graphs for which there is a large degeneracy of the single particle ground states and where the projector onto the space of single particle ground states is highly reducible.…

Despite nearly a century of study of the $S=1/2$ Heisenberg model on the square lattice, there is still disagreement on the nature of its high-energy excitations. By tuning toward the Heisenberg model from the exactly soluble Ising limit,…

An important step towards a comprehensive understanding of far-from-equilibrium dynamics of quantum many-body systems is the identification of unifying features that are independent of microscopic details of the system. We experimentally…

We find novel confined states in the spin-$S$ nearest-neighbor antiferromagnetic Heisenberg model on the two-dimensional Penrose lattice. Linear spin waves have massively degenerate eigenstates strictly confined to tricoordinated sites.…

We describe dynamics of transverse spin-helix state (SHS) -- a product state with spatially rotating magnetization -- under anisotropic Heisenberg XXZ spin chain evolution. Due to experimental relevance we especially focus on magnetization…

Frustrated quantum magnets may exhibit fascinating collective phenomena. The main goal of this dissertation is to provide conclusive evidence for the emergence of novel phases of matter like quantum spin liquids in local quantum spin…

We investigate the quantum Heisenberg model on the pyrochlore lattice for a generic spin $S$ in the presence of nearest-neighbor $J_{1}$ and second-nearest-neighbor $J_{2}$ exchange interactions. By employing the pseudofermion functional…

We consider some classical and frustrated lattice spin models with global O(3) spin symmetry. There is no general analytical method to find a ground-state if the spin dependence of the Hamiltonian is more than quadratic (i.e. beyond the…

We generalize the Matrix Product States method using the chiral vertex operators of Conformal Field Theory and apply it to study the ground states of the XXZ spin chain, the J1-J2 model and random Heisenberg models. We compute the overlap…

We investigate the two-dimensional frustrated quantum Heisenberg model with bond disorder on nearest-neighbor couplings using the recently introduced Foundation Neural-Network Quantum States framework, which enables accurate and efficient…

In Heisenberg models with exchange anisotropy, transverse spin components are not conserved and can decay not only by transport, but also by dephasing. Here we utilize ultracold atoms to simulate the dynamics of 1D Heisenberg spin chains,…

The electron Hamiltonian of narrow semiconductor rings with the Rashba and Dresselhaus spin orbit terms is invariant under time-reversal operation followed by a large gauge transformation. We find that all the eigenstates are doubly…

Understanding extreme non-locality in many-body quantum systems can help resolve questions in thermostatistics and laser physics. The existence of symmetry selection rules for Hamiltonians with non-decaying terms on infinite-size lattices…

In the framework of the Landau-Lifshitz equations without any dissipation (an approximation which may also be helpful for finite but weak Gilbert damping), with all interactions included, for general ground states, geometries and domain…

The search for exotic quantum spin liquid states in simple yet realistic spin models remains a central challenge in the field of frustrated quantum magnetism. Here we consider the canonical nearest-neighbor kagome Heisenberg antiferromagnet…

We study the consequences of in-plane (D_p) and out-of-plane (D_z) Dzyaloshinsky-Moriya (DM) interactions on the thermodynamic properties of spin-1/2} Heisenberg model on the kagome lattice using numerical linked cluster expansions and…

Using the matrix product formalism, we introduce a two parameter family of exactly solvable $xyz$ spin 1/2 Heisenberg chains in magnetic field (with nearest neighbor interactions) and calculate the ground state and correlation functions in…

We study a matrix product state (MPS) algorithm to approximate excited states of translationally invariant quantum spin systems with periodic boundary conditions. By means of a momentum eigenstate ansatz generalizing the one of \"Ostlund…

In many frustrated Ising models, a single-spin flip dynamics is frozen out at low temperatures compared to the dominant interaction energy scale because of the discrete "multiple valley" structure of degenerate ground-state manifold. This…

Density matrix renormalization group (DMRG) calculations on large systems (up to 3096 spins) indicate that the ground state of the Heisenberg model on a 3-chain Kagome strip is spontaneously dimerized. This system has degenerate ground…