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First-order phase transitions produce abrupt changes to the character of both ground and excited electronic states. Here we conduct electronic compressibility measurements to map the spin phase diagram and Landau level (LL) energies of monolayer${\mathrm{WSe}}_2$in a magnetic field. We resolve a sequence of first-order phase transitions between completely spin-polarized LLs and states with LLs of both spins. Unexpectedly, the LL gaps are roughly constant over a wide range of magnetic fields below the transitions, which we show reflects spin-polarized ground states with opposite spin excitations. These transitions also extend into compressible regimes, with a sawtooth boundary between full and partial spin polarization. We link these observations to the important influence of LL filling on the exchange energy beyond a smooth density-dependent contribution. Our results show that${\mathrm{WSe}}_2$realizes a unique hierarchy of energy scales where such effects induce reentrant magnetic phase transitions tuned by density and magnetic field.

Published by the American Physical Society2024 

We study a simple electron-phonon model on square and triangular versions of the Lieb lattice using an asymptotically exact strong coupling analysis. At zero temperature and electron density n 1/4 1 (one electron per unit cell), for various ranges of parameters in the model, we exploit a mapping to the quantum dimer model to establish the existence of a spin-liquid phase with Z(2) topological order (on the triangular lattice) and a multicritical line corresponding to a quantum critical spin liquid (on the square lattice). In the remaining part of the phase diagram, we find a host of charge-density-wave phases (valence-bond solids), a conventional s-wave superconducting phase, and with the addition of a small Hubbard U to tip the balance, a phonon-induced d-wave superconducting phase. Under a special condition, we find a hidden pseudospin SUo2 thorn symmetry that implies an exact constraint on the superconducting order parameters. 

A pair-density-wave (PDW) is a superconducting state with an oscillating order parameter. A microscopic mechanism that can give rise to it has been long sought but has not yet been established by any controlled calculation. Here we report a density-matrix renormalization-group (DMRG) study of an effectivet-J-Vmodel, which is equivalent to the Holstein-Hubbard model in a strong-coupling limit, on long two-, four-, and six-leg triangular cylinders. While a state with long-range PDW order is precluded in one dimension, we find strong quasi-long-range PDW order with a divergent PDW susceptibility as well as the spontaneous breaking of time-reversal and inversion symmetries. Despite the strong interactions, the underlying Fermi surfaces and electron pockets around theKand$${K}^{\prime}$$$K^{\prime }$points in the Brillouin zone can be identified. We conclude that the state is valley-polarized and that the PDW arises from intra-pocket pairing with an incommensurate center of mass momentum. In the two-leg case, the exponential decay of spin correlations and the measured central chargec ≈ 1 are consistent with an unusual realization of a Luther-Emery liquid.