Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2604.25992

Towards a microscopic model for an electronic quantum charge liquid

Jacob R. Taylor, Sankar Das Sarma, Seth Musser

cond-mat.str-elcond-mat.stat-mechquant-phSubmitted Apr 28, 2026• Announced Apr 30, 2026• 0 citations
arXivHTMLPDF

Abstract

We provide a route to constructing an electronic quantum charge liquid (QCL), a state made up of fermions at fractional filling of a lattice that does not break translation. Starting with spinless fermions at filling $ν=3/2$ we pair them to get bosons at filling $ν=3/4$ per unit cell. The tetramer model, a generalization of the dimer model, on the square lattice is evaluated as a candidate bosonic QCL at filling $ν= 3/4$. It is shown that these models exhibit a local $\mathbb{Z}_4$ symmetry. Upon numerical study of a family of tetramer wavefunctions it is found that while one is gapless due to $\mathrm{U}(1)^3$ symmetry at least one other can be definitively shown to be gapped. The gapped nature of this state, along with its $\mathbb{Z}_4$ symmetry, leads us to propose that it is an example of the elusive bosonic QCL displaying the minimal $\mathbb{Z}_4$ topological order. We conclude by discussing possible extensions to other lattice geometries, electronic QCLs, and to Rydberg atoms.

Comments
8 pages, 6 figures

Related papers

Fractionalization as an alternate to charge ordering in electronic insulators

Seth Musser, Meng Cheng, T. Senthil

Who ordered anyons? Though exotic, anyons can be required by a system's fractional symmetry response. For example, in gapped systems with U(1) and unbroken translation symmetry, fractional lattice filling leads to anyons via the LSM constraint. The authors analyze here this setting and, for a given filling, determine the minimal number of required anyons. They prove this minimal topological order is unique and dub it a ``quantum charge liquid'' (QCL). The authors conclude by discussing the phenomenology of QCLs.

arXiv:2408.03984•Physical review. B./Physical review. B•Jun 2, 2025•8 citations

Classification and emergence of quantum spin liquids in chiral Rydberg models

Poetri Sonya Tarabunga, Giuliano Giudici, Titas Chanda +1 more

We investigate the nature of quantum phases arising in chiral interacting Hamiltonians recently realized in Rydberg atom arrays. We classify all possible fermionic chiral spin liquids with $\mathrm{U}(1)$ global symmetry using parton construction on the honeycomb lattice. The resulting classification includes six distinct classes of gapped quantum spin liquids: the corresponding variational wavefunctions obtained from two of these classes accurately describe the Rydberg many-body ground state at $1/2$ and $1/4$ particle density. Complementing this analysis with tensor network simulations, we conclude that both particle filling sectors host a spin liquid with the same topological order of a $\ensuremath{\nu}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}1/2$ fractional quantum Hall effect. At density $1/2$, our results clarify the phase diagram of the model, while at density $1/4$, they provide an explicit construction of the ground-state wavefunction with almost unit overlap with the microscopic one. These findings pave the way to the use of parton wavefunctions to guide the discovery of quantum spin liquids in chiral Rydberg models.

arXiv:2303.12829•Physical review. B./Physical review. B•Aug 7, 2023•6 citations

Defect mediated quantum melting of charge ordered insulators

Abijith Krishnan, Ajesh Kumar, T. Senthil

Two-dimensional (2d) electronic systems on a lattice at fractional filling $ν= p/q$ exhibit a competition between charge ordered insulators, called Wigner-Mott insulators (WMIs), at large Coulomb repulsion and Fermi-liquid metals at large electronic kinetic energy. When those two energy scales are roughly equal, insulating states that restore the lattice translation symmetry, which we call quantum charge liquids (QCLs), may emerge. When gapped, these QCLs must exhibit topological order. In this work, we show that the allowed topological ordered phases that are proximate to the WMI strongly depend on the charge ordering in the WMI. In particular, we show that when $q$ is even, no direct transition exists between a WMI with the smallest allowed unit cell size from filling constraints, i.e., the "minimal" WMI, and the topological order with the smallest ground state degeneracy on a torus allowed by filling constraints, i.e., the "minimal" TO. Furthermore, we describe the quantum melting transition of the WMIs to the proximate QCLs in terms of the proliferation of the topological defects of the WMIs. The field theory of this transition in terms of the topological defects reveals their role as precursors to the anyon excitations in the QCLs.

arXiv:2510.00099•Sep 30, 2025•0 citations

Symmetry-protected gapless Z2 spin liquids

Yuan-Ming Lu

Despite rapid progress in understanding gapped topological states, much less is known about gapless topological phases of matter, especially in strongly correlated electrons. In this work, we discuss a large class of robust gapless quantum spin liquids in frustrated magnets made of half-integer spins, which are described by gapless fermionic spinons coupled to dynamical ${\mathbb{Z}}_{2}$ gauge fields. Requiring $\text{U}(1)$ spin conservation, time-reversal, and certain space-group symmetries, we show that certain spinon symmetry fractionalization class necessarily leads to a gapless spectrum. These gapless excitations are stable against any perturbations, as long as the required symmetries are preserved. Applying these gapless criteria to spin-$\frac{1}{2}$ systems on square, triangular, and kagome lattices, we show that all gapped symmetric ${\mathbb{Z}}_{2}$ spin liquids in Abrikosov-fermion representation can also be realized in Schwinger-boson representation. This leads to 64 gapped ${\mathbb{Z}}_{2}$ spin liquids on square lattice, and 8 gapped states on both kagome and triangular lattices.

arXiv:1606.05652•Physical review. B./Physical review. B•Mar 19, 2018•12 citations

Chiral spin liquid from magnetic Wannier states

I. Panfilov, Adarsh S. Patri, Kun Yang +1 more

We present a mapping of a two-dimensional system of interacting bosons in a strong perpendicular magnetic field to an equivalent system of interacting bosons on the square lattice in the absence of the field. The mapping utilizes a magnetic Bloch and the corresponding magnetic Wannier single-particle basis in the lowest Landau level. By construction, the ground states of the resulting model of interacting bosons on the square lattice are gapped fractionalized liquids or gapless Bose metal states with broken time-reversal symmetry at specific rational filling fractions.

arXiv:1601.00968•Physical review. B./Physical review. B•Mar 16, 2016•1 citation

Nematic spin liquid phase in a frustrated spin-1 system on the square lattice

Wen-Jun Hu, Shou-Shu Gong, Hsin-Hua Lai +3 more

Frustration in quantum spin systems promote a variety of novel quantum phases. An important example is the frustrated spin-1 model on the square lattice with the nearest-neighbor bilinear (${J}_{1}$) and biquadratic (${K}_{1}$) interactions. We provide strong evidence for a nematic spin liquid phase in a range of ${K}_{1}/{J}_{1}$ near the SU(3)-symmetric point (${J}_{1}={K}_{1}$), based on the linear flavor-wave theory and extensive density matrix renormalization group calculation. This phase displays no spin dipolar or quadrupolar order, preserves translational symmetry but spontaneously breaks ${C}_{4}$ lattice rotational symmetry, and possesses fluctuations peaked at the wave vector $(\ensuremath{\pi},2\ensuremath{\pi}/3)$. The spin excitation gap drops rapidly with system size and appears to be gapless, and the nematic order is attributed to the dominant $(\ensuremath{\pi},2\ensuremath{\pi}/3)$ fluctuations. Our results provide a novel mechanism for electronic nematic order and, more generally, open up a new avenue to explore frustration-induced exotic ground states.

arXiv:1711.06523•Physical review. B./Physical review. B•Oct 28, 2019•16 citations
We provide a route to constructing an electronic quantum charge liquid (QCL), a state made up of fermions at fractional filling of a lattice that does not break translation. Starting with spinless fermions at filling ν=3/2ν=3/2ν=3/2 we pair them to get bosons at filling ν=3/4ν=3/4ν=3/4 per unit cell. The tetramer model, a generalization of the dimer model, on the square lattice is evaluated as a candidate bosonic QCL at filling ν=3/4ν= 3/4ν=3/4. It is shown that these models exhibit a local Z4\mathbb{Z}_4Z4​ symmetry. Upon numerical study of a family of tetramer wavefunctions it is found that while one is gapless due to U(1)3\mathrm{U}(1)^3U(1)3 symmetry at least one other can be definitively shown to be gapped. The gapped nature of this state, along with its Z4\mathbb{Z}_4Z4​ symmetry, leads us to propose that it is an example of the elusive bosonic QCL displaying the minimal Z4\mathbb{Z}_4Z4​ topological order. We conclude by discussing possible extensions to other lattice geometries, electronic QCLs, and to Rydberg atoms.
Who ordered anyons? Though exotic, anyons can be required by a system's fractional symmetry response. For example, in gapped systems with U(1) and unbroken translation symmetry, fractional lattice filling leads to anyons via the LSM constraint. The authors analyze here this setting and, for a given filling, determine the minimal number of required anyons. They prove this minimal topological order is unique and dub it a ``quantum charge liquid'' (QCL). The authors conclude by discussing the phenomenology of QCLs.
We investigate the nature of quantum phases arising in chiral interacting Hamiltonians recently realized in Rydberg atom arrays. We classify all possible fermionic chiral spin liquids with U(1)\mathrm{U}(1)U(1) global symmetry using parton construction on the honeycomb lattice. The resulting classification includes six distinct classes of gapped quantum spin liquids: the corresponding variational wavefunctions obtained from two of these classes accurately describe the Rydberg many-body ground state at 1/21/21/2 and 1/41/41/4 particle density. Complementing this analysis with tensor network simulations, we conclude that both particle filling sectors host a spin liquid with the same topological order of a $\ensuremath{\nu}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}1/2$ fractional quantum Hall effect. At density 1/21/21/2, our results clarify the phase diagram of the model, while at density 1/41/41/4, they provide an explicit construction of the ground-state wavefunction with almost unit overlap with the microscopic one. These findings pave the way to the use of parton wavefunctions to guide the discovery of quantum spin liquids in chiral Rydberg models.
Two-dimensional (2d) electronic systems on a lattice at fractional filling ν=p/qν= p/qν=p/q exhibit a competition between charge ordered insulators, called Wigner-Mott insulators (WMIs), at large Coulomb repulsion and Fermi-liquid metals at large electronic kinetic energy. When those two energy scales are roughly equal, insulating states that restore the lattice translation symmetry, which we call quantum charge liquids (QCLs), may emerge. When gapped, these QCLs must exhibit topological order. In this work, we show that the allowed topological ordered phases that are proximate to the WMI strongly depend on the charge ordering in the WMI. In particular, we show that when qqq is even, no direct transition exists between a WMI with the smallest allowed unit cell size from filling constraints, i.e., the "minimal" WMI, and the topological order with the smallest ground state degeneracy on a torus allowed by filling constraints, i.e., the "minimal" TO. Furthermore, we describe the quantum melting transition of the WMIs to the proximate QCLs in terms of the proliferation of the topological defects of the WMIs. The field theory of this transition in terms of the topological defects reveals their role as precursors to the anyon excitations in the QCLs.
Despite rapid progress in understanding gapped topological states, much less is known about gapless topological phases of matter, especially in strongly correlated electrons. In this work, we discuss a large class of robust gapless quantum spin liquids in frustrated magnets made of half-integer spins, which are described by gapless fermionic spinons coupled to dynamical Z2{\mathbb{Z}}_{2}Z2​ gauge fields. Requiring U(1)\text{U}(1)U(1) spin conservation, time-reversal, and certain space-group symmetries, we show that certain spinon symmetry fractionalization class necessarily leads to a gapless spectrum. These gapless excitations are stable against any perturbations, as long as the required symmetries are preserved. Applying these gapless criteria to spin-12\frac{1}{2}21​ systems on square, triangular, and kagome lattices, we show that all gapped symmetric Z2{\mathbb{Z}}_{2}Z2​ spin liquids in Abrikosov-fermion representation can also be realized in Schwinger-boson representation. This leads to 64 gapped Z2{\mathbb{Z}}_{2}Z2​ spin liquids on square lattice, and 8 gapped states on both kagome and triangular lattices.
We present a mapping of a two-dimensional system of interacting bosons in a strong perpendicular magnetic field to an equivalent system of interacting bosons on the square lattice in the absence of the field. The mapping utilizes a magnetic Bloch and the corresponding magnetic Wannier single-particle basis in the lowest Landau level. By construction, the ground states of the resulting model of interacting bosons on the square lattice are gapped fractionalized liquids or gapless Bose metal states with broken time-reversal symmetry at specific rational filling fractions.
Frustration in quantum spin systems promote a variety of novel quantum phases. An important example is the frustrated spin-1 model on the square lattice with the nearest-neighbor bilinear (J1{J}_{1}J1​) and biquadratic (K1{K}_{1}K1​) interactions. We provide strong evidence for a nematic spin liquid phase in a range of K1/J1{K}_{1}/{J}_{1}K1​/J1​ near the SU(3)-symmetric point (J1=K1{J}_{1}={K}_{1}J1​=K1​), based on the linear flavor-wave theory and extensive density matrix renormalization group calculation. This phase displays no spin dipolar or quadrupolar order, preserves translational symmetry but spontaneously breaks C4{C}_{4}C4​ lattice rotational symmetry, and possesses fluctuations peaked at the wave vector $(\ensuremath{\pi},2\ensuremath{\pi}/3)$. The spin excitation gap drops rapidly with system size and appears to be gapless, and the nematic order is attributed to the dominant $(\ensuremath{\pi},2\ensuremath{\pi}/3)$ fluctuations. Our results provide a novel mechanism for electronic nematic order and, more generally, open up a new avenue to explore frustration-induced exotic ground states.