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arXiv:2305.13355

Continuous Wigner-Mott transition at $ν=1/5$

Thomas G. Kiely, Debanjan Chowdhury

Published May 22, 2023• 0 citations
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Abstract

Electrons can organize themselves into charge-ordered states to minimize the effects of long-ranged Coulomb interactions. In the presence of a lattice, commensurability constraints lead to the emergence of incompressible Wigner-Mott insulators at various rational electron fillings, $ν~=p/q$. The mechanism for quantum fluctuation-mediated melting of the Mott insulators with increasing electron kinetic energy remains an outstanding problem. Here, using matrix product state techniques, we analyze the bandwidth-tuned transition out of the Wigner-Mott insulator at $ν=1/5$ in an extended Hubbard model on infinite cylinders of varying circumference. For the two-leg ladder, the transition from the Mott insulator to the Luttinger liquid proceeds via a distinct intermediate phase with gapless Cooper-pairs and gapped electronic excitations. The resulting Luther-Emery liquid is the analog of a strongly fluctuating superconductor. We place these results in the context of a low-energy bosonization based theory for the transition. On the five-leg cylinder, we provide numerical evidence for a direct continuous transition between the Wigner-Mott insulator and a metallic phase across which the spin and charge-gaps vanish simultaneously. We comment on the connections to ongoing experiments in dual-gated bilayer moiré transition metal dichalcogenide materials.

DOI
10.48550/arxiv.2305.13355

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Continuous Wigner-Mott transition at ν=1/5ν=1/5ν=1/5
Electrons can organize themselves into charge-ordered states to minimize the effects of long-ranged Coulomb interactions. In the presence of a lattice, commensurability constraints lead to the emergence of incompressible Wigner-Mott insulators at various rational electron fillings, ν =p/qν~=p/qν =p/q. The mechanism for quantum fluctuation-mediated melting of the Mott insulators with increasing electron kinetic energy remains an outstanding problem. Here, using matrix product state techniques, we analyze the bandwidth-tuned transition out of the Wigner-Mott insulator at ν=1/5ν=1/5ν=1/5 in an extended Hubbard model on infinite cylinders of varying circumference. For the two-leg ladder, the transition from the Mott insulator to the Luttinger liquid proceeds via a distinct intermediate phase with gapless Cooper-pairs and gapped electronic excitations. The resulting Luther-Emery liquid is the analog of a strongly fluctuating superconductor. We place these results in the context of a low-energy bosonization based theory for the transition. On the five-leg cylinder, we provide numerical evidence for a direct continuous transition between the Wigner-Mott insulator and a metallic phase across which the spin and charge-gaps vanish simultaneously. We comment on the connections to ongoing experiments in dual-gated bilayer moiré transition metal dichalcogenide materials.
We study theoretically the quantum phase transition from a metal to a Wigner-Mott insulator at fractional commensurate filling on a two-leg ladder. We show that a continuous transition out of a symmetry-preserving Luttinger liquid metal is possible where the onset of insulating behavior is accompanied by the breaking of the lattice translation symmetry. At fillings $\ensuremath{\nu}=1/m$ per spin per unit cell, we find that the spin degrees of freedom also acquire a gap at the Wigner-Mott transition for odd integer mmm. In contrast for even integer mmm, the spin sector remains gapless and the resulting insulator is a ladder analog of the two-dimensional spinon surface state. In both cases, a charge neutral spinless mode remains gapless across the Wigner-Mott transition. We discuss physical properties of these transitions and comment on insights obtained for thinking about continuous Wigner-Mott transitions in two-dimensional systems which are being studied in moire materials.
We develop a theory for a continuous bandwidth-tuned transition at fixed fractional electron filling from a metal with a generic Fermi surface to a ``Wigner-Mott'' insulator that spontaneously breaks crystalline space-group symmetries. Across the quantum critical point, (i) the entire electronic Fermi surface disappears abruptly upon approaching from the metallic side, and (ii) the insulating charge gap and various order parameters associated with the spontaneously broken space-group symmetries vanish continuously upon approaching from the insulating side. Additionally, the insulating side hosts a Fermi surface of neutral spinons. We present a framework for describing such continuous metal-insulator transitions (MITs) and analyze the example of a bandwidth-tuned transition at a filling, $\ensuremath{\nu}=1/6$, for spinful electrons on the triangular lattice. By extending the theory to a certain large-NNN limit, we provide a concrete example of such a continuous MIT and discuss numerous experimental signatures near the critical point. We place our results in the context of recent experiments in moir\'e transition metal dichalcogenide materials.
A lightly doped single-band Hubbard model on a two-leg ladder exhibits a Luther-Emery phase, whereas the three-band Hubbard ladder behaves as a Luttinger liquid upon hole doping. To understand this discrepancy, we present a systematic density-matrix renormalization group study of the three-band Hubbard model on two-leg cylinders with further-neighbor particle hoppings. The inclusion of the longer-range hopping is motivated by the studies of the single-band Hubbard model in which the further-neighbor hopping terms are suggested to be crucial for the unconventional superconductivity. When the longer-range hopping parameters are small, the ground state is a Luttinger liquid having mutually commensurate superconducting, charge, and spin density wave correlations. Increasing the longer-range hopping drives a transition into a Luther-Emery phase with quasi-long-ranged superconducting and charge orders but short-ranged spin-spin correlations. By down-folding the three-band Hubbard model into an effective $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}J\text{\ensuremath{-}}{J}^{\ensuremath{'}}$ model, we find that in the Luther-Emery phase, both the nearest- and second-neighbor kinetic energies are enhanced due to an effective increase of copper-oxygen hybridization. Amplifying intercell oxygen orbital hopping mirrors the benefits of reducing the charge transfer energy, causing doped holes to favor oxygen orbitals and strengthening superconducting pairing.
Abstract We present a T = 0 K renormalization group (RG) phase diagram for the electronic Hubbard model in two dimensions on the square lattice at half filling. The RG procedure treats quantum fluctuations in the single particle occupation number nonperturbatively via the unitarily decoupling of one electronic state at every RG step. The resulting phase diagram thus possesses the quantum fluctuation energy scale (ω) as one of its axes. A relation is derived between ω and the effective temperature scale upto which gapless, as well as emergent gapped phases can be obtained. We find that the normal and insulating phases of the half-filled Hubbard model correspond, for any on-site repulsion, to a marginal Fermi liquid normal phase and a topologically-ordered gapped Mott insulating liquid respectively. The marginal Fermi liquid is found to arise from singular forward scattering in directions normal to the nested Fermi surface, while singular backscattering events lead to Mott liquid state. The transition between these two phases involves passage through a pseudogapped phase bookended by Fermi surface topology-changing Lifshitz transitions. The pseudogap phase is observed to arise from the electronic differentiation encoded within the nested Fermi surface, and involves the gradual gapping of the Fermi surface from antinodes to nodes via charge and spin excitations that are mutually entangled. We obtain effective Hamiltonians for various phases, as well as wavefunctions for the low-energy many-body eigenstates of the Mott liquid. Benchmarking of the ground-state energy per particle and the double-occupancy fraction for the Mott liquid against existing numerical results yields excellent agreement. Presence of a Néel ordering symmetry-breaking perturbation in the RG leads to an antiferromagnetic spin-ordered charge insulating Mott state. Our results thus offer novel insights on a variety of aspects of the Mott–Hubbard problem, and can be extended to the doped system.
Motivated by recent experiments on ultracold fermionic spin-1/2 6^66Li atoms in a Lieb lattice at various Hubbard repulsion UUU and filling fractions nnn (Lebrat et al., arXiv:2404.17555), we conduct a density matrix renormalization group (DMRG) analysis of the Hubbard model on a two-leg Lieb ladder. At half-filling, we find a ferrimagnetic Mott insulating ground state, consistent with Lieb's theorem. Away from half-filling, a state with finite total spin S⃗2≠0\vec{S}^2 \neq 0S2=0 and vanishing charge gap persists down to filling nc≈2/3n_c \approx 2/3nc​≈2/3. For lower, incommensurate fillings, the system is described by a Luttinger liquid with one charge and one spin mode. Intriguingly, in a narrow window near nc=2/3n_c = 2/3nc​=2/3, close to the onset of ferromagnetic order, we identify a superconducting Luther-Emery phase with dominant sxys_{xy}sxy​-wave pairing.
A lightly doped single-band Hubbard model on a two leg ladder exhibits a Luther-Emery phase, while the three-band Hubbard ladder behaves as a Luttinger liquid upon hole doping. In order to understand this discrepancy, we present a systematic density-matrix renormalization group study of the three-band Hubbard model on two-leg cylinders with further-neighbor particle hoppings. The inclusion of the longer-range hopping is motivated by the studies of the single-band Hubbard model in which the further-neighbor hopping terms are suggested to be crucial for the unconventional superconductivity. When the longer-range hopping parameters are small, the ground state is a Luttinger liquid having mutually commensurate superconducting, charge and spin density wave correlations. Increasing the longer-range hopping drives a transition into a Luther-Emery phase with quasi-long ranged superconducting and charge orders but short-ranged spin-spin correlations. By down-folding the three-band Hubbard model into an effective ttt-t′t't′-JJJ-J′J'J′ model, we find that in the Luther-Emery phase, both the nearest and second neighbor kinetic energies are enhanced due to an effective increase of copper-oxygen hybridization. Amplifying inter-cell oxygen orbital hopping mirrors the benefits of reducing the charge transfer energy, causing doped holes to favor oxygen orbitals and strengthening superconducting pairing.