Type-II heavy Fermi liquids and the magnetic memory of 4Hb-TaS2_2

The interplay of quantum spin liquids with itinerant conduction electrons is of crucial interest for understanding layered structures composed of frustrated magnet and metal monolayers. Using parton-mean-field theory, we here demonstrate that a type-II heavy Fermi liquid, which is characterized by a vortex lattice in the slave boson condensate, can occur in the vicinity of the quantum phase transition separating fractionalized and heavy Fermi liquid phases. The magnetic flux threading each such vortex is about $v_f/ 137 c$ times smaller than the magnetic flux threading vortices in type-II superconductors, where $v_f$ is the speed of magnetic excitations and $c$ the speed of light. This makes a magnetic observation of this effect challenging. We propose scanning tunneling spectroscopy instead and investigate its signatures. If a type-II heavy Fermi liquid is cooled into a type-II superconductor, vortices in the slave boson condensate and in the superconducting condensate mutually attract. We argue that the type-II heavy Fermi liquid thereby provides a compelling explanation for the magnetic memory observed recently [Persky \textit{et al.}, Nature \textbf{609}, 692 (2022)] in thermal cycles of 4Hb-TaS$_2$.Comment: 4+$\epsilon$ pages, 9 pages supplement. 2 + 2 figures. Typos, formatting and reference list update

ZN\mathbb{Z}_N lattice gauge theories with matter fields

Motivated by the exotic phenomenology of certain quantum materials and recent advances in programmable quantum emulators, we here study fermions and bosons in $\mathbb Z_N$ lattice gauge theories. We introduce a family of exactly soluble models, and characterize their orthogonal (semi-)metallic ground states, the excitation spectrum, and the correlation functions. We further study integrability breaking perturbations using an appropriately derived set of Feynman diagrammatic rules and borrowing physics associated to Anderson's orthogonality catastrophe. In the context of the ground states, we revisit Luttinger's theorem following Oshikawa's flux insertion argument and furthermore demonstrate the existence of a Luttinger surface of zeros in the fermionic Green's function. Upon inclusion of perturbations, we address the transition from the orthogonal metal to the normal state by condensation of certain excitations in the gauge sectors, so-called ``$e$-particles''. We furthermore discuss the effect of dynamics in the dual ``$m$-particle'' excitations, which ultimately leads to the formation of charge-neutral hadronic $N$-particle bound states. We present analytical arguments for the most important phases and estimates for phase boundaries of the model. Specifically, and in sharp distinction to quasi-1D $\mathbb Z_N$ lattice gauge theories, renormalization group arguments imply that the phase diagram does not include an emergent deconfining $U(1)$ phase. Therefore, in regards to lattice QED problems, $\mathbb Z_N$ quantum emulators with $N<\infty$ can at best be used for approximate solutions at intermediate length scales

Soluble limit and criticality of fermions in Z2\mathbb Z_2 gauge theories

Quantum information theory and strongly correlated electron systems share a common theme of macroscopic quantum entanglement. In both topological error correction codes and theories of quantum materials (spin liquid, heavy fermion and high-$T_c$ systems) entanglement is implemented by means of an emergent gauge symmetry. Inspired by these connections, we introduce a simple model for fermions moving in the deconfined phase of a $\mathbb Z_2$ gauge theory, by coupling Kitaev's toric code to mobile fermions. This permits us to exactly solve the ground state of this system and map out its phase diagram. Reversing the sign of the plaquette term in the toric code, permits us to tune the groundstate between an orthogonal metal and an orthogonal semimetal, in which gapless quasiparticles survive despite a gap in the spectrum of original fermions. The small-to-large Fermi surface transition between these two states occurs in a stepwise fashion with multiple intermediate phases. By using a novel diagrammatic technique we are able to explore physics beyond the integrable point, to examine various instabilities of the deconfined phase and to derive the critical theory at the transition between deconfined and confined phases. We outline how the fermionic toric code can be implemented as a quantum circuit thus providing an important link between quantum materials and quantum information theory.Comment: 6 pages with 6 figures + Appendix. Main update since v1: Proposal for a quantum emulator for fermions in $\mathbb Z_2$ gauge theories. Main update since v2: Extended discussion of orthogonal semimetal-metal transition. v2 is accepted for publication in Phys.Rev.