Emergent phenomena in frustrated spin systems

This thesis deals with frustration effects in spin models. An analytical study of critical phenomena in three-dimensional hyperbolic space is undertaken and a new critical fixed point is shown to exist. Moreover, the so-called "windmill spin model" is studied using various Monte Carlo algorithms and analytical calculations

Thermodynamics of two-dimensional bosons in the lowest Landau level

We study the thermodynamics of short-range interacting, two-dimensional bosons constrained to the lowest Landau level. When the temperature is higher than other energy scales of the problem, the partition function reduces to a multidimensional complex integral that can be handled by classical Monte Carlo techniques. This approach takes the quantization of the lowest Landau level orbits fully into account. We observe that the partition function can be expressed in terms of a function of a single combination of thermodynamic variables, which allows us to derive exact thermodynamic relations. We determine the asymptotic behavior of this function and compute some thermodynamic observables numerically.Comment: 7 pages, 5 figures. A supplementary video is found via this https://youtu.be/4-nOKptY75w YouTube lin

Quantum phases of two-dimensional Z2\mathbb{Z}_2 gauge theory coupled to single-component fermion matter

We investigate the rich quantum phase diagram of Wegner's theory of discrete Ising gauge fields interacting with $U(1)$ symmetric single-component fermion matter hopping on a two-dimensional square lattice. In particular limits the model reduces to (i) pure $\mathbb{Z}_2$ even and odd gauge theories, (ii) free fermions in a static background of deconfined $\mathbb{Z}_2$ gauge fields, (iii) the kinetic Rokhsar-Kivelson quantum dimer model at a generic dimer filling. We develop a local transformation that maps the lattice gauge theory onto a model of $\mathbb{Z}_2$ gauge-invariant spin $1/2$ degrees of freedom. Using the mapping, we perform numerical density matrix renormalization group calculations that corroborate our understanding of the limits identified above. Moreover, in the absence of the magnetic plaquette term, we reveal signatures of topologically ordered Dirac semimetal and staggered Mott insulator phases at half-filling. At strong coupling, the lattice gauge theory displays fracton phenomenology with isolated fermions being completely frozen and dimers exhibiting restricted mobility. In that limit, we predict that in the ground state dimers form compact clusters, whose hopping is suppressed exponentially in their size. We determine the band structure of the smallest clusters numerically using exact diagonalization. The rich phenomenology discussed in this paper can be probed in analog and digital quantum simulators of discrete gauge theories and in Kitaev spin-orbital liquids.Comment: v3: intro now includes a summary of main results together with a new Fig. 1; new results for the confinement transition in the inset of Fig. 10; references adde

Enhanced nematic fluctuations near the Mott insulating phase of high-Tc cuprates

The complexity of the phase diagram of the cuprates goes well beyond its unique high-Tc superconducting state, as it hosts a variety of different electronic phenomena, such as the pseudogap, nematic order, charge order, and strange metallic behavior. The parent compound, however, is well understood as a Mott insulator, displaying quenched charge degrees of freedom and low-energy antiferromagnetic excitations described by the Heisenberg exchange coupling J. Here we show that doping holes in the oxygen orbitals inevitably generates another spin interaction - a biquadratic coupling - that must be included in the celebrated t−J model. While this additional interaction does not modify the linear spin wave spectrum, it promotes an enhanced nematic susceptibility that is peaked at a temperature scale determined by J. Our results explain several puzzling features of underdoped YBa2Cu3O7, such as the proximity of nematic and antiferromagnetic order, the anisotropic magnetic incommensurability, and the in-plane resistivity anisotropy. Furthermore, it naturally accounts for the absence of nematicity in electron-doped cuprates, and supports the idea that the pseudogap temperature is related to strong local antiferromagnetism

Quantum Scar States in Coupled Random-Graph Models

We analyze the Hilbert space connectivity of the $L$ site PXP-model by constructing the Hamiltonian matrices via a Gray code numbering of basis states. Once constructed, the matrices reveal a simple structure: they are all formed out of a single Hamiltonian-path backbone and side-connections. The PXP model is known for the presence of scar states in the middle of the spectrum that have area-law entanglement. The understanding that we develop of the PXP-model's adjacency graph equips us with a general instruction on how to construct a class of Hamiltonians with tunable constraint degree and variable network topology. We explore a version of this model where the network topology is constructed around a random-graph model. We find two classes of weakly-entangled mid-spectrum eigenstates. The first class are scars that are near-product eigenstates of the subsystems, while the second class has $\log 2$ entanglement entropy and is tied to the occurrence of special types of subgraphs. The latter states have some resemblance to the Lin-Motrunich $\sqrt{2}$-scars.Comment: 13 pages, 9 figure