Charge transfer excitations, pair density waves, and superconductivity in moiré materials

Transition-metal dichalcogenide (TMD) bilayers are a new class of tunable moiré systems attracting interest as quantum simulators of strongly interacting electrons in two dimensions. In particular, recent theory predicts that the correlated insulator observed in WSe₂/WS₂ at half filling is a charge-transfer insulator similar to cuprates and, upon further hole doping, exhibits a transfer of charge from anionlike to cationlike orbitals at different locations in the moiré unit cell. In this work, we demonstrate that in this doped charge-transfer insulator, tightly bound charge-2e excitations can form to lower the total electrostatic repulsion. This composite excitation, which we dub a trimer, consists of a pair of holes bound to a charge-transfer exciton. When the bandwidth of doped holes is small, trimers crystallize into insulating pair density waves at a sequence of commensurate doping levels. When the bandwidth becomes comparable to the pair binding energy, itinerant holes and charge-2e trimers interact resonantly, leading to unconventional superconductivity similar to superfluidity in an ultracold Fermi gas near Feshbach resonance. Our theory is broadly applicable to strongly interacting charge-transfer insulators, such as WSe₂/WS₂ or TMD homobilayers under an applied electric field

A Simple Mechanism for Unconventional Superconductivity in a Repulsive Fermion Model

Motivated by a scarcity of simple and analytically tractable models of superconductivity from strong repulsive interactions, we introduce a simple tight-binding lattice model of fermions with repulsive interactions that exhibits unconventional superconductivity (beyond BCS theory). The model resembles an idealized conductor-dielectric-conductor trilayer. The Cooper pair consists of electrons on opposite sides of the dielectric, which mediates the attraction. In the strong coupling limit, we use degenerate perturbation theory to show that the model reduces to a superconducting hard-core Bose-Hubbard model. Above the superconducting critical temperature, an analog of pseudo-gap physics results where the fermions remain Cooper paired with a large single-particle energy gap.Comment: 12+12 pages; 3 figures; v5 is a major revision with new additions: a conductor-dielectric-conductor trilayer interpretation, an elaborated introduction, figures 1 and 2, and sections 4.3.1 and 5.

Foliated Field Theory and String-Membrane-Net Condensation Picture of Fracton Order

Foliated fracton order is a qualitatively new kind of phase of matter. It is similar to topological order, but with the fundamental difference that a layered structure, referred to as a foliation, plays an essential role and determines the mobility restrictions of the topological excitations. In this work, we introduce a new kind of field theory to describe these phases: a foliated field theory. We also introduce a new lattice model and string-membrane-net condensation picture of these phases, which is analogous to the string-net condensation picture of topological order.Comment: 22+15 pages, 8 figures; v3 added a summary of our model near the end of the introductio

Foliated fracton order in the checkerboard model

In this work, we show that the checkerboard model exhibits the phenomenon of foliated fracton order. We introduce a renormalization group transformation for the model that utilizes toric code bilayers as an entanglement resource, and show how to extend the model to general three-dimensional manifolds. Furthermore, we use universal properties distilled from the structure of fractional excitations and ground-state entanglement to characterize the foliated fracton phase and find that it is the same as two copies of the X-cube model. Indeed, we demonstrate that the checkerboard model can be transformed into two copies of the X-cube model via an adiabatic deformation.Comment: 8 pages, 9 figure

Universal entanglement signatures of foliated fracton phases

Fracton models exhibit a variety of exotic properties and lie beyond the conventional framework of gapped topological order. In a previous work, we generalized the notion of gapped phase to one of foliated fracton phase by allowing the addition of layers of gapped two-dimensional resources in the adiabatic evolution between gapped three-dimensional models. Moreover, we showed that the X-cube model is a fixed point of one such phase. In this paper, according to this definition, we look for universal properties of such phases which remain invariant throughout the entire phase. We propose multi-partite entanglement quantities, generalizing the proposal of topological entanglement entropy designed for conventional topological phases. We present arguments for the universality of these quantities and show that they attain non-zero constant value in non-trivial foliated fracton phases.Comment: 17 pages, 7 figure

Fast Tensor Disentangling Algorithm

Many recent tensor network algorithms apply unitary operators to parts of a tensor network in order to reduce entanglement. However, many of the previously used iterative algorithms to minimize entanglement can be slow. We introduce an approximate, fast, and simple algorithm to optimize disentangling unitary tensors. Our algorithm is asymptotically faster than previous iterative algorithms and often results in a residual entanglement entropy that is within 10 to 40% of the minimum. For certain input tensors, our algorithm returns an optimal solution. When disentangling order-4 tensors with equal bond dimensions, our algorithm achieves an entanglement spectrum where nearly half of the singular values are zero. We further validate our algorithm by showing that it can efficiently disentangle random 1D states of qubits.Comment: 8+4 pages, 3 figures; v3 improves the extended algorithm in Appendix

Quantum Gauge Networks: A New Kind of Tensor Network

Although tensor networks are powerful tools for simulating low-dimensional quantum physics, tensor network algorithms are very computationally costly in higher spatial dimensions. We introduce quantum gauge networks: a different kind of tensor network ansatz for which the computation cost of simulations does not explicitly increase for larger spatial dimensions. We take inspiration from the gauge picture of quantum dynamics, which consists of a local wavefunction for each patch of space, with neighboring patches related by unitary connections. A quantum gauge network (QGN) has a similar structure, except the Hilbert space dimensions of the local wavefunctions and connections are truncated. We describe how a QGN can be obtained from a generic wavefunction or matrix product state (MPS). All $2k$-point correlation functions of any wavefunction for $M$ many operators can be encoded exactly by a QGN with bond dimension $O(M^k)$. In comparison, for just $k=1$, an exponentially larger bond dimension of $2^{M/6}$ is generically required for an MPS of qubits. We provide a simple QGN algorithm for approximate simulations of quantum dynamics in any spatial dimension. The approximate dynamics can achieve exact energy conservation for time-independent Hamiltonians, and spatial symmetries can also be maintained exactly. We benchmark the algorithm by simulating the quantum quench of fermionic Hamiltonians in up to three spatial dimensions.Comment: 11+9 pages, 6+1 figures. v3 adds Figs 3 and 4 and Eq 7 to extract a density matrix from the QG