About

Walter Metzner is a Professor in the Department of Integrative Biology and Physiology at UCLA College of Life Sciences. His research interests include sensory processing and motor control, with a particular focus on auditory feedback control of vocalization. He has a background in zoology, having earned his B.S. from the University of Erlangen in Germany in 1981, and his M.S. and Ph.D. degrees from the University of Munich, Germany, in 1984 and 1989 respectively. Dr. Metzner's work contributes to understanding the neural mechanisms underlying sensory and motor functions, especially in the context of behavioral neuroscience and neuroethology.

Research topics

• Quantum mechanics
• Physics
• Condensed matter physics
• Theoretical physics
• Statistical physics

Selected publications

• Coexisting magnetic, charge, and superconducting orders in the two-dimensional Hubbard model

  ArXiv.org · 2026-01-01

  articleOpen access

  We perform a renormalized mean-field study of the two-dimensional repulsive Hubbard model, focusing on the intricate interplay and possible coexistence of magnetic, charge, and superconducting orders. We improve on conventional mean-field theory by utilizing a renormalization group framework that captures high-energy fluctuations. This method generates effective magnetic and $d$-wave pairing interactions, and allows for an unbiased exploration of coexisting phases at weak and moderate interaction strengths. Unrestricted mean-field calculations of the effective Hamiltonian on large finite lattices are combined with analyses in the thermodynamic limit, revealing a rich phase diagram with extensive regions of coexisting orders. We find that $d$-wave superconductivity coexists with Néel order on the electron-doped side. On the hole-doped side, superconductivity is found to coexist with spiral or stripe magnetic orders. Within the stripe ordered region, the superconducting order parameter is spatially modulated, with a period that follows the charge modulation of the stripes. Below van Hove filling, pairing provides the primary energy gain, while the stripe order yields only a small, and hence fragile, additional energy lowering.

  PublisherOA PDF

• SU(2) gauge theory of fluctuating stripe order in the two-dimensional Hubbard model

  ArXiv.org · 2026-03-13

  articleOpen accessSenior author

  We present an SU(2) gauge theory of fluctuating stripe order in the two-dimensional Hubbard model. The theory is based on a fractionalization of the electron operators in fermionic chargons with a pseudospin degree of freedom, and charge neutral spinons capturing fluctuations of the spin orientation. The chargons are treated in a renormalized mean-field theory. We focus on regions of the phase diagram where they undergo stripe order. The spinons are described by a non-linear sigma model with pseudospin stiffnesses determined by the chargons. They prevent breaking of the physical SU(2) spin symmetry at any finite temperature, resulting in a charge ordered pseudogap phase with a reconstructed Fermi surface and a spin gap. The spectral function for single-particle excitations exhibits a collection of Fermi arcs and other structures. The arcs appear in various regions of the Brillouin zone, but never exclusively around the Brillouin zone diagonals.

  PublisherOA PDF

• Coexisting magnetic, charge, and superconducting orders in the two-dimensional Hubbard model

  arXiv (Cornell University) · 2026-02-23

  preprintOpen access

  We perform a renormalized mean-field study of the two-dimensional repulsive Hubbard model, focusing on the intricate interplay and possible coexistence of magnetic, charge, and superconducting orders. We improve on conventional mean-field theory by utilizing a renormalization group framework that captures high-energy fluctuations. This method generates effective magnetic and $d$-wave pairing interactions, and allows for an unbiased exploration of coexisting phases at weak and moderate interaction strengths. Unrestricted mean-field calculations of the effective Hamiltonian on large finite lattices are combined with analyses in the thermodynamic limit, revealing a rich phase diagram with extensive regions of coexisting orders. We find that $d$-wave superconductivity coexists with Néel order on the electron-doped side. On the hole-doped side, superconductivity is found to coexist with spiral or stripe magnetic orders. Within the stripe ordered region, the superconducting order parameter is spatially modulated, with a period that follows the charge modulation of the stripes. Below van Hove filling, pairing provides the primary energy gain, while the stripe order yields only a small, and hence fragile, additional energy lowering.

  PublisherDOI

• SU(2) gauge theory of fluctuating stripe order in the two-dimensional Hubbard model

  arXiv (Cornell University) · 2026-03-13

  preprintOpen accessSenior author

  We present an SU(2) gauge theory of fluctuating stripe order in the two-dimensional Hubbard model. The theory is based on a fractionalization of the electron operators in fermionic chargons with a pseudospin degree of freedom, and charge neutral spinons capturing fluctuations of the spin orientation. The chargons are treated in a renormalized mean-field theory. We focus on regions of the phase diagram where they undergo stripe order. The spinons are described by a non-linear sigma model with pseudospin stiffnesses determined by the chargons. They prevent breaking of the physical SU(2) spin symmetry at any finite temperature, resulting in a charge ordered pseudogap phase with a reconstructed Fermi surface and a spin gap. The spectral function for single-particle excitations exhibits a collection of Fermi arcs and other structures. The arcs appear in various regions of the Brillouin zone, but never exclusively around the Brillouin zone diagonals.

  PublisherDOI

• Collective mode spectroscopy in time-reversal symmetry breaking superconductors

  Physical review. B./Physical review. B · 2025-10-15 · 1 citations

  articleOpen access

  Collective excitations in superconductors provide essential insights into the symmetry of the broken phase, acting as indicators for identifying the ground state gap symmetry. Time-reversal symmetry breaking (TRSB) superconductors exhibit a rich spectrum of collective modes due to the complexity of their order parameters. These modes, known as “generalized clapping modes,” draw analogies to the clapping modes of helium-3 phase A. This study investigates two-dimensional TRSB superconductors with an order parameter of the form <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi mathvariant="normal">Δ</a:mi> <a:mo>=</a:mo> <a:msub> <a:mi mathvariant="normal">Δ</a:mi> <a:mn>1</a:mn> </a:msub> <a:mo>+</a:mo> <a:mi>i</a:mi> <a:msub> <a:mi mathvariant="normal">Δ</a:mi> <a:mn>2</a:mn> </a:msub> </a:mrow> </a:math> , exploring the characteristics of their collective mode spectrum. We begin with a phenomenological Ginzburg-Landau approach to build intuition, then develop a dynamical theory by deriving linearized equations of motion using the pseudospin formalism. Beyond the linear regime, we propose a classification scheme based on the potential to induce (an)isotropic oscillations in the superconducting condensate. By perturbing the system in symmetry channels distinct from the ground state, we aim to selectively enhance or suppress different mode responses. This study analyzes the features of these generalized clapping modes as a function of the ratio between the order parameter components under various excitation schemes. We believe that our findings could help distinguish between different order parameter symmetries in TRSB superconducting condensates and estimate the magnitude of their components.

  PublisherDOI

• Collective mode spectroscopy in time-reversal symmetry breaking superconductors

  ArXiv.org · 2025-03-11

  preprintOpen access

  Time-reversal symmetry breaking (TRSB) superconductors show a rich collective mode spectrum. In general, collective excitations in superconductors can provide crucial information on the symmetry of the broken phase, in particular, serving as a fingerprint for determining the groundstate gap symmetry. In this work, we consider several even parity two-dimensional TRSB superconductors characterized by an order parameter of the form $Δ= Δ_1 + iΔ_2$. We provide a classification scheme of the collective excitations in the above systems as a function of the ratio between the components $Δ_1/Δ_2$. In order to excite the modes in the systems we have adopted two different probes: a quench of the condensate symmetry and a finite momentum transfer induced by an external electric field. Both methods allow us to excite and characterize the different modes in the spectra. To further interpret the results of the numerical calculations we provide a Ginzburg-Landau analysis and we construct a dynamical theory, deriving the linearized equations of motion in the pseudospin formalism. Our results could help distinguish between different order parameters symmetries of a TRSB superconducting condensate and estimate the magnitude of its different components.

  PublisherOA PDFDOI

• Spin stiffnesses and stability of magnetic order in the lightly doped two-dimensional Hubbard model

  ArXiv.org · 2025-04-16

  preprintOpen accessSenior author

  We analyze the density dependence of the spin stiffnesses and the stability of magnetic order with respect to quantum fluctuations in the two-dimensional Hubbard model close to half-filling. The stiffnesses are computed from the spin susceptibility obtained from a random phase approximation in a magnetically ordered state. For a sizable next-to-nearest neighbor hopping amplitude and a moderate Hubbard interaction, the mean-field ground state is a Néel antiferromagnet in the electron doped regime at and above half-filling, and a planar circular spiral state in the hole doped regime below half-filling. Upon electron doping, the Néel stiffness decreases smoothly and not very steeply. By contrast, the in-plane and out-of-plane stiffnesses in the spiral state drop abruptly at half-filling. The out-of-plane stiffness even drops to zero, and then increases again very slowly upon increasing hole doping. At finite temperatures, the Néel-to-spiral transition is shifted into the hole doped regime, the stiffnesses are continuous functions of the density, and they vanish at the transition. For small hole doping, the spin stiffnesses describe the quantum fluctuations only in a small momentum range, which shrinks to zero upon approaching half-filling. Using the above results, we show that the quantum ground state of the lightly electron doped Hubbard model remains Néel ordered, while quantum fluctuations probably destroy the spiral long-range order in the hole doped regime, giving rise to a quantum disordered state with a spin gap.

  PublisherOA PDFDOI

• Spin susceptibility in a pseudogap state with fluctuating spiral magnetic order

  ArXiv.org · 2025-09-09

  preprintOpen accessSenior author

  We compute the electron spin susceptibility in the pseudogap regime of the two-dimensional Hubbard model in the framework of a SU(2) gauge theory of fluctuating magnetic order. The electrons are fractionalized in fermionic chargons with a pseudospin degree of freedom and bosonic spinons. The chargons are treated in a renormalized mean-field theory and order in a Néel or spiral magnetic state in a broad range around half-filling below a transition temperature $T^*$. Fluctuations of the spin orientation are captured by the spinons. Their dynamics is governed by a non-linear sigma model, with spin stiffnesses computed microscopically from the pseudospin susceptibility of the chargons. The SU(2) gauge group is higgsed in the chargon sector, and the spinon fluctuations prevent breaking of the physical spin symmetry at any finite temperature. The electron spin susceptibility obtained from the gauge theory shares many features with experimental observations in the pseudogap regime of cuprate superconductors: the dynamical spin susceptibility $S(\mathbf{q},ω)$ has a spin gap, the static uniform spin susceptibility $κ_s$ decreases strongly with temperature below $T^*$, and the NMR relaxation rate $T_1^{-1}$ vanishes exponentially in the low temperature limit if the ground state is quantum disordered. At low hole doping, $S(\mathbf{q},ω)$ exhibits nematicity below a transition temperature $T_{\rm nem} &lt; T^*$, and at larger hole doping in the entire pseudogap regime below $T^*$.

  PublisherOA PDFDOI

• Spiral to stripe transition in the two-dimensional Hubbard model

  Physical review. B./Physical review. B · 2024-06-27 · 8 citations

  preprintOpen access

  We obtain an almost complete understanding of the mean-field phase diagram of the two-dimensional Hubbard model on a square lattice with a sizable next-nearest-neighbor hopping and a moderate interaction strength. In particular, we clarify the nature of the transition region between the spiral and the stripe phase. Complementing previous [] real-space Hartree-Fock calculations on large finite lattices, we solve the mean-field equations for coplanar unidirectional magnetic order directly in the thermodynamic limit, and we determine the nature of the magnetic states right below the mean-field critical temperature <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msup><a:mi>T</a:mi><a:mo>*</a:mo></a:msup></a:math> by a Landau free-energy analysis. While the magnetic order for filling factors <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>n</b:mi><b:mo>≥</b:mo><b:mn>1</b:mn></b:mrow></b:math> is always of Néel type, for <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>n</c:mi><c:mo>≤</c:mo><c:mn>1</c:mn></c:mrow></c:math> the following sequence of magnetic states is found as a function of increasing hole-doping: Néel, planar circular spiral, multispiral, and collinear spin-charge stripe states. Multispiral states are superpositions of several spirals with distinct wave vectors, and lead to concomitant charge order. We finally point out that nematic and charge orders inherited from the magnetic order can survive even in the presence of fluctuations, and we present a corresponding qualitative phase diagram. Published by the American Physical Society 2024

  PublisherDOI

• Marginal Fermi liquid behavior at the onset of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>2</mml:mn><mml:msub><mml:mi>k</mml:mi><mml:mi>F</mml:mi></mml:msub></mml:mrow></mml:math> density wave order in two-dimensional metals with flat hot spots

  Physical review. B./Physical review. B · 2024-06-05 · 1 citations

  preprintOpen accessSenior author

  We analyze quantum fluctuation effects at the onset of incommensurate <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mn>2</a:mn><a:msub><a:mi>k</a:mi><a:mi>F</a:mi></a:msub></a:mrow></a:math> charge- or spin-density-wave order in two-dimensional metals for a model in which the ordering wave vector <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi mathvariant="bold">Q</b:mi></b:math> connects a single pair of hot spots on the Fermi surface with a vanishing Fermi surface curvature. The tangential momentum dependence of the bare dispersion near the hot spots is proportional to <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mrow><d:mo>|</d:mo></d:mrow><d:msub><d:mi>k</d:mi><d:mi>t</d:mi></d:msub><d:msup><d:mrow><d:mo>|</d:mo></d:mrow><d:mi>α</d:mi></d:msup></d:mrow></d:math> with <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mi>α</e:mi><e:mo>&gt;</e:mo><e:mn>2</e:mn></e:mrow></e:math>. We first compute the order parameter susceptibility and the fermion self-energy in a random phase approximation (RPA). Logarithmic divergences are subsequently treated by a renormalization-group analysis. The coupling between the order parameter fluctuations and the fermions vanishes logarithmically in the low-energy limit. As a consequence, the logarithmic divergences found in the RPA do not sum up to anomalous power laws. Instead, only logarithmic corrections to Fermi liquid behavior are obtained. In particular, the quasiparticle weight and the Fermi velocity vanish logarithmically at the hot spots. Published by the American Physical Society 2024

  PublisherOA PDFDOI

Recent grants

• NIH Grant R29DC002538

  NIH · $474k · 2001

• NIH Grant R01DC005400

  NIH · $922k · 2008

Frequent coauthors

• Jiang Feng

  Jilin Agricultural University

  35 shared

• Shuyi Zhang

  Huizhou Central People's Hospital

  25 shared

• V. Meden

  RWTH Aachen University

  19 shared

• Steffen R. Hage

  University of Tübingen

  17 shared

• Tinglei Jiang

  Northeast Normal University

  17 shared

• Hiroyuki Yamase

  National Institute for Materials Science

  16 shared

• K. Schönhammer

  University of Göttingen

  14 shared

• D. Vollhardt

  Max Planck Institute for Polymer Research

  14 shared

Education

• Ph.D., Biology

  University of California, Los Angeles

  1987

• B.S., Biology

  University of California, Los Angeles

  1982