Degenerate two-dimensional electron liquids are theoretically established to possess two vastly distinct collisional electron mean free paths, where even-parity deformations of the Fermi surface are hydrodynamic with a short collisional mean free path but odd-parity deformations remain near ballistic (known as the “tomographic” transport regime). Predicted signatures of this regime rely on the scaling of observables with temperature or device dimension, both of which are difficult to establish with certainty. Here, we consider magnetotransport in a minimal model of tomographic electrons and show that even a small magnetic field suppresses tomographic transport signatures and thus acts as a sensitive and unique probe of this regime. Fundamentally, the magnetic field breaks time-reversal invariance, which is a prerequisite for the odd-even parity effect in the collisional relaxation. We analyze in detail the scaling of the transverse conductivity, which has been linked to small-channel conductance of interaction-dominated electrons, and show that a tomographic scaling regime at intermediate wave numbers is quickly suppressed with magnetic field to a hydrodynamic or collisionless form. We confirm that the suppression occurs at relatively small magnetic fields when the cyclotron radius is comparable to the ballistic mean free path of the dominant odd-parity mode. This occurs at a much smaller magnetic field than the magnetic field strength required to suppress hydrodynamic electron transport, which suggests an experimental protocol to extract the odd-parity mean free path.

We highlight the exotic quantum criticality of quasi-two-dimensional single-component fermions at half filling that are minimally coupled to a dynamical Ising gauge theory. With the numerical matrix product state based infinite density matrix renormalization group method, we discover a robust quantum critical line in the infinite cylinder geometry, where gauge confinement and dimerized translation symmetry breaking emerge simultaneously. We investigate how the transition can be split by a topologically ordered dimerized phase that is stabilized by additional short-range repulsive interactions. We conjecture a 𝑢⁡(1) deconfined criticality scenario, propose a corresponding low-energy effective field theory of the exotic quantum critical point in the two-dimensional limit, and identify its shortcomings.

We construct an effective field theory describing the collective Tkachenko oscillation mode of a vortex lattice in a two-dimensional rotating Bose-Einstein condensate in the long-wavelength regime. The theory has the form of a noncommutative field theory of a Nambu-Goldstone boson, which exhibits a noncommutative version of dipole symmetry. From the effective field theory, we show that, at zero temperature, the decay width Γ of the Tkachenko mode scales with its energy E as Γ∼E³ in the low-energy limit. We also discuss the width of the Tkachenko mode at a small temperature.

Despite a long history of studies of vortex crystals in rotating superfluids, their melting due to quantum fluctuations is poorly understood. Here we develop a fracton-elasticity duality to investigate a two-dimensional vortex lattice within the fast rotation regime, where the Lifshitz model of the collective Tkachenko mode serves as the leading-order low-energy effective theory. We incorporate topological defects and discuss several quantum melting scenarios triggered by their proliferation. Furthermore, we lay the groundwork for a dual non-linear emergent gravity description of the superfluid vortex crystals.

Emergent gauge theories take a prominent role in the description of quantum matter, supporting deconfined phases with topological order and fractionalized excitations. A common construction of Z2 lattice gauge theories, first introduced by Wegner, involves Ising gauge spins placed on links and subject to a discrete Z2 Gauss law constraint. As shown by Kitaev, Z2 lattice gauge theories also emerge in the exact solution of certain spin systems with bond-dependent interactions. In this context, the Z2 gauge field is constructed from Majorana fermions, with gauge constraints given by the parity of Majorana fermions on each site. In this work, we provide an explicit Jordan-Wigner transformation that maps between these two formulations on the square lattice, where the Kitaev-type gauge theory emerges as the exact solution of a spin-orbital (Kugel-Khomskii) Hamiltonian. We then apply our mapping to study local perturbations to the spin-orbital Hamiltonian, which correspond to anisotropic interactions between electric-field variables in the Z2 gauge theory. These are shown to induce anisotropic confinement that is characterized by emergence of weakly-coupled one-dimensional spin chains. We study the nature of these phases and corresponding confinement transitions in both absence and presence of itinerant fermionic matter degrees of freedom. Finally, we discuss how our mapping can be applied to the Kitaev spin-1/2 model on the honeycomb lattice.

We investigate the interplay of quantum one-dimensional discrete ℤ₂ gauge fields and fermion matter near full filling in terms of deconfined fractionalized hole excitations that constitute mobile domain walls between vacua that break spontaneously translation symmetry. In the limit of strong string tension, we uncover emergent integrable correlated hopping dynamics of holes which is complementary to the constrained XXZ description in terms of bosonic dimers. We analyze numerically quantum dynamics of spreading of an isolated hole together with the associated time evolution of entanglement and provide analytical understanding of its salient features. We also study the model enriched with a short-range interaction and clarify the nature of the resulting ground state at low filling of holes and identify deconfined hole excitations near the hole filling 𝜈^ℎ=1/3.