About

Leon Balents is a Professor and KITP Permanent Member at the Department of Physics, UC Santa Barbara. His research interests focus on developing theory to uncover and explain exotic quantum phenomena in the real world. He is part of the Condensed Matter Theory group, where his work contributes to advancing the understanding of complex quantum systems and their underlying principles.

Research topics

• Artificial Intelligence
• Physics
• Computer Science
• Quantum mechanics
• Condensed matter physics

Selected publications

• Identifying Instabilities with Quantum Geometry in Flat-Band Systems

  Physical Review Letters · 2026-04-07

  preprintOpen access

  The absence of a well-defined Fermi surface in flat-band systems challenges the conventional understanding of instabilities toward Landau order based on nesting. We investigate the existence of an intrinsic nesting structure encoded in the band geometry [i.e., the wave functions of the flat band(s)], which leads to a maximal susceptibility at the mean-field level and, thus, determines the instability toward ordered phases. More generally, we show that, for a given band structure and observable, we can define two vector fields: one which corresponds to the Bloch vector of the projection operator onto the manifold of flat bands and another which is "dressed" by the observable. The overlap between the two vector fields, possibly shifted by a momentum vector Q, fully determines the mean-field susceptibility of the corresponding order parameter. When the overlap is maximized, so is the susceptibility, and this geometrically corresponds to "perfect nesting" of the band structure. In that case, we show that the correlation length of this order parameter, even for Q≠0, is entirely characterized by a generalized quantum metric in an intuitive manner and is, therefore, lower bounded in topologically nontrivial bands. As an example, we demonstrate hidden nesting for staggered antiferromagnetic spin order in an exactly flat-band model, which is notably different from the general intuition that flat bands are closely associated with ferromagnetism. We check the actual emergence of this long-range order using the determinantal quantum Monte Carlo algorithm. Additionally, we demonstrate that a Fulde-Ferrell-Larkin-Ovchinnikov-like state (pairing with nonzero center of mass momentum) can arise in flat bands upon breaking time-reversal symmetry, even if Zeeman splitting is absent.

  PublisherOA PDFDOI

• Spin excitation continuum from degenerate states in the mixed ferro-antiferromagnetic exchange system CeMgAl ₁₁ O ₁₉

  Science Advances · 2026-03-06

  preprintOpen accessCorresponding

  In the search for unconventional magnetism, exotic quantum states are characterized by a lack of order and a broad spin excitation continuum approaching zero temperature. We study the two-dimensional triangular-lattice effective spin- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mrow> </mml:math> system CeMgAl 11 O 19 , which shows slight disorder but no magnetic ordering down to 100 millikelvin. Spin-wave analysis in the magnetic-field–polarized state determines the spin Hamiltonian featuring a mixed ferromagnetic-antiferromagnetic nearest-neighbor exchange interaction [ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>J</mml:mi> <mml:mi>z</mml:mi> </mml:msub> </mml:mrow> </mml:math> = −0.024(5) milli–electron volts, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>J</mml:mi> <mml:mo>⊥</mml:mo> </mml:msub> </mml:mrow> </mml:math> = 0.056(3) milli–electron volts]. This places the system near an exactly solvable point of the spin- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:mrow> </mml:math> triangular-lattice XXZ model ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>J</mml:mi> <mml:mi>z</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> <mml:msub> <mml:mi>J</mml:mi> <mml:mo>⊥</mml:mo> </mml:msub> </mml:mrow> </mml:math> ) with extensive ground-state degeneracy. In zero field, neutron spectroscopy reveals a prominent continuum; we show that this arises from an ensemble average of spin-wave spectra across the degenerate ground-state manifold. This demonstrates that the role of weak quenched disorder can be quantitatively constrained: It inhibits unique ground-state selection and stabilizes a local distribution within the degenerate manifold, yielding continuum-like spectra that necessitate a critical reevaluation of the experimental signatures of exotic quantum states.

  PublisherDOI

• Distinct Optical Excitation Mechanisms of a Coherent Magnon in a van der Waals Antiferromagnet

  Physical Review Letters · 2025-02-10 · 8 citations

  article

  The control of antiferromagnets with ultrashort optical pulses has emerged as a prominent field of research. Tailored laser excitation can launch coherent spin waves at terahertz frequencies, yet a comprehensive description of their generation mechanisms is still lacking despite extensive efforts. Using terahertz emission spectroscopy, we investigate the generation of a coherent magnon mode in the van der Waals antiferromagnet NiPS_{3} under a range of photoexcitation conditions. By tuning the pump photon energy from transparency to resonant with a d-d transition, we reveal a striking change in the coherent magnon's dependence on the pump polarization, indicating two distinct excitation mechanisms. Our findings provide a strategy for the manipulation of magnetic modes via photoexcitation around subgap electronic states.

  PublisherDOI

• Emergent Hidden Multipolar State in the Triangular Lattice Magnet TmZn2GaO5

  ArXiv.org · 2025-03-27

  preprintOpen access

  TmZn2GaO5 is a newly synthesized triangular lattice magnet that exhibits a unique quantum phase characterized by strong Ising anisotropy, a pseudo-doublet crystal electric field ground state, and a low-energy gapped excitation at the K point. Unlike its well-known counterparts, TmMgGaO4 and YbMgGaO4, this material crystallizes in a distinct hexagonal structure, leading to a cleaner platform for investigating frustrated magnetism. Magnetic susceptibility, heat capacity, and inelastic neutron scattering measurements confirm the absence of long-range magnetic order down to 50 mK, placing TmZn2GaO5 in a distinct region of the transverse-field Ising model phase diagram. Theoretical calculations based on spin-wave theory and mean-field modeling reproduce key experimental observations, reinforcing the material's placement in a quantum disordered/multipolar state. These results highlight its potential for exploring quantum disordered states, anisotropic excitations, and exotic quantum phases in frustrated spin systems.

  PublisherOA PDFDOI

• Emergent gauge flux in mixed QED$_3$ with flavor chemical potential: application to magnetized U(1) Dirac spin liquids

  ArXiv.org · 2025-08-11 · 1 citations

  preprintOpen access

  We design a lattice model of a "mixed" U(1) gauge field coupled to fermions with a flavor chemical potential and solve it with large-scale determinant quantum Monte Carlo simulations, For zero flavor chemical potential, the model realizes three-dimensional quantum electrodynamics (QED$_3$) which has been argued to describe the ground state and low-energy excitations of the Dirac spin liquid phase of quantum antiferromagnets. At finite flavor chemical potential, corresponding to a Zeeman field perturbing the Dirac spin liquid, we find a "chiral flux" phase which is characterized by the generation of a finite mean emergent gauge flux and, accordingly, the formation of relativistic Landau levels for the Dirac fermions. In this state, the U(1)$_m$ magnetic symmetry is spontaneously broken, leading to a gapless free photon mode which, due to spin-flux-attachment, is observable in the longitudinal spin structure factor. We numerically compute longitudinal and transverse spin structure factors which match our continuum and lattice mean-field theory predictions. In a different region of the phase diagram, strong fluctuations of the emergent gauge field give rise to an antiferromagnetically ordered state with gapped Dirac fermions coexisting with a deconfined gauge field. We also find an interesting intermediate phase where the chiral flux phase and the antiferromagnetic phase coexist. We argue that our results pave the way to testable predictions for magnetized Dirac spin liquids in frustrated quantum antiferromagnets.

  PublisherOA PDFDOI

• Spin Seebeck effect of interacting spinons

  Physical review. B./Physical review. B · 2025-08-04 · 1 citations

  article

  We present the theory of the longitudinal spin Seebeck effect between a Heisenberg spin-$1/2$ chain and a conductor. The effect consists of the generation of a spin current across the spin chain-conductor interface in response to the temperature difference between the two systems. In this setup, the current is given by the convolution of the local spin susceptibilities of the spin chain and the conductor. We find the spin current to be fully controlled, both in the magnitude and the sign, by the backscattering interaction between spinons, fractionalized spin excitations of the Heisenberg chain. In particular, it vanishes when the spinons form a noninteracting spinon gas. Our analytical results for the local spin susceptibility at the open end of the spin chain are in excellent agreement with numerical density matrix renormalization group simulations.

  PublisherDOI

• Topological Chiral Superconductivity in the Triangular-Lattice Hofstadter-Hubbard Model

  ArXiv.org · 2025-09-02

  preprintOpen access

  Moiré materials provide exciting platforms for studying the interplay of strong electronic correlation and large magnetic flux effects. We study the lightly doped Hofstadter-Hubbard model on a triangular lattice through large-scale density matrix renormalization group and determinantal quantum Monte Carlo simulations. We find strong evidence for a robust chiral superconducting (SC) phase with dominant power-law pairing correlations and a quantized spin Chern number. The SC phase emerges at very weak interaction and grows stronger at intermediate interaction strengths (U ) for a wide range of hole doping. We also discuss the possible distinct nature of the normal state in different U regimes. Our work provides theoretical insights into the emergence of topological superconductivity from doping topological Chern bands or magnetic flux induced chiral spin liquid states of Moiré materials.

  PublisherOA PDFDOI

• Gyrotropic magnetic effect in metallic chiral magnets

  arXiv (Cornell University) · 2025-04-28

  preprintOpen accessSenior author

  We study the gyrotropic magnetic effect (GME), the low-frequency limit of optical gyrotropy, in metals and semimetals coupled to chiral spin textures. In these systems, the chiral spin texture which lacks inversion symmetry can imprint itself upon the electronic structure through Hund's coupling, leading to novel low-frequency optical activity. Using perturbation theory and numerical diagonalization of both relativistic and non-relativistic models of conduction electrons coupled to spin textures, we analyze how the GME manifests in both single-$q$ and multi-$q$ textures. Analytical expressions for the rotatory power are derived in terms of universal scaling functions. Estimates based on realistic material parameters reveal an experimentally viable range of values for the rotatory power. The GME arises from the orbital and spin magnetic moments of conduction electrons, with the orbital part closely tied to Berry curvature and playing a significant role in relativistic metals but not so in non-relativistic metals where there is no inherent Berry curvature. The spin contribution to the GME can be significant in non-relativistic metals with a large Fermi energy. Our work establishes the GME as a sensitive probe of magnetic chirality and symmetry breaking in metallic chiral magnets.

  PublisherOA PDFDOI

• Emergent magnetism and spin liquids in an extended Hubbard description of moiré bilayers

  ArXiv.org · 2025-05-09

  preprintOpen access

  Motivated by twisted transition metal dichalcogenides (TMDs), we study an extended Hubbard model with both on-site and off-site repulsive interactions, in which Mott insulating states with concomitant charge order occur at fractional fillings. To resolve the charge ordering as well as the fate of the local moments formed thereby, we perform large-scale density matrix renormalization group calculations on cylindrical geometries for several filling fractions and ranges of interaction strength. Depending on the precise parameter regime, both antiferromagnetically ordered as well as quantum-disordered states are found, with a particularly prominent example being a quantum spin liquid-type ground state on top of charge-ordering with effective Kagomé geometry. We discuss the different mechanisms at play in stabilizing various electronic and magnetic states. The results suggest that moiré TMDs are a promising venue for emergent quantum magnetism of strongly interacting electrons.

  PublisherOA PDFDOI

• Spin-Charge Bound States and Emerging Fermions in a Quantum Spin Liquid

  PRX Quantum · 2025-10-24 · 2 citations

  articleOpen access

  The complex interplay between charge and spin dynamics lies at the heart of strongly correlated quantum materials, and it is a fundamental topic in basic research with far-reaching technological perspectives. We explore in this paper the dynamics of holes in a single-band, extended <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>t</a:mi> </a:math> - <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>J</c:mi> </c:math> model where the background spins form a <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mrow> <e:mi mathvariant="double-struck">Z</e:mi> </e:mrow> <e:mn>2</e:mn> </e:msub> </e:math> quantum spin liquid. Using a field theory approach based on a parton construction, we show that while the electrons for most momenta fractionalize into uncorrelated charge-carrying holons and spin-carrying spinons as generally expected for a quantum spin liquid, the spinon-holon scattering cross section diverges for certain momenta, signaling strong correlations. By deriving an effective low-energy Hamiltonian describing this dynamics, we demonstrate that these divergences are due to the formation of long-lived spinon-holon bound states. Since the wave function of these bound states is localized over a few lattice sites, they correspond to well-defined fermions with the same charge and spin as the underlying electrons. We then show that quantum gas microscopy with atoms in optical lattices provides an excellent platform for verifying and probing the internal spatial structure of these emerging fermions. The fermions will furthermore show up as clear quasiparticle peaks in angle-resolved photoemission spectroscopy with an intensity determined by their internal structure. For a nonzero hole concentration, the fermions form hole pockets with qualitatively the same location, shape, and intensity variation in the Brillouin zone as the so-called Fermi arcs observed in the pseudogap phase. Such agreement is remarkable since the Fermi arcs arise from the delicate interplay between the symmetry of the quantum spin liquid and the internal structure of the emerging fermions in a minimal single-band model with no extra degrees of freedom added. Our results, therefore, provide a microscopic mechanism for the conjectured fractionalized Fermi liquid and open up new pathways for exploring the pseudogap phase and high-temperature superconductivity as arising from a quantum spin liquid.

  PublisherDOI

Recent grants

• Quantum Phenomena in Solids

  NSF · $354k · 2015–2019

• Quantum phenomena in solids

  NSF · $345k · 2012–2016

• Quantum Phenomena in Solids

  NSF · $360k · 2018–2021

• Quantum Phenomena in Solids

  NSF · $400k · 2021–2024

• Quantum Phenomena in Solids

  NSF · $330k · 2008–2012

Frequent coauthors

• L. Savary

  University of California, Santa Barbara

  190 shared

• Jianpeng Liu

  ShanghaiTech University

  138 shared

• J. G. Checkelsky

  130 shared

• J. W. Lynn

  127 shared

• T. Suzuki

  Shibaura Institute of Technology

  66 shared

• T. Suzuki

  62 shared

• Matthew P. A. Fisher

  53 shared

• Gang Chen

  Collaborative Innovation Center of Quantum Matter

  41 shared

Labs

• Leon Balents's LabPI

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Education

• B.S., Physics and Mathematics

  Massachusetts Institute of Technology

• Ph.D., Physics

  Harvard University

  1994

Awards & honors

• Fellow of the American Physical Society
• Member of the American Academy of Arts and Sciences
• Member of the National Academy of Sciences