The moving Born–Oppenheimer approximation

Proceedings of the National Academy of Sciences · 2026-02-13

We develop a mixed quantum-classical framework, dubbed the moving Born–Oppenheimer approximation (MBOA), to describe the dynamics of slow degrees of freedom (DOFs) coupled to fast ones. As in the Born–Oppenheimer approximation (BOA), the fast degrees of freedom adiabatically follow a state that depends on the slow ones. Unlike the BOA, this state depends on both the positions and the momenta of the slow DOFs. We study several model systems: a spin-1/2 particle and a spinful molecule moving in a spatially inhomogeneous magnetic field, and a gas of fast particles coupled to a piston. The MBOA reveals rich dynamics for the slow degree of freedom, including reflection, dynamical trapping, and mass renormalization. It also significantly modifies the state of the fast DOFs. For example, the spins in the molecule are entangled and squeezed, while the gas of fast particles develops gradients that are synchronized with the motion of the piston for a long time. The MBOA can be used to describe both classical and quantum systems and has potential applications in quantum chemistry, correlated materials, atomic physics, molecular dynamics, and quantum sensing.

Phase Space Fractons

Physical Review Letters · 2026-03-04

Perhaps the simplest approach to constructing models with subdimensional particles or fractons is to require the conservation of dipole or higher multipole moments. We generalize this approach to allow for moments in phase space and classify all possible classical fracton models with phase-space multipole conservation laws. We focus on a new self-dual model that conserves both dipole and quadrupole moments in position and momentum; we analyze its dynamics and find quasiperiodic orbits in phase space that evade ergodic exploration of the full phase space.

The moving Born–Oppenheimer approximation

Proceedings of the National Academy of Sciences · 2026-02-13 · 2 citations

We develop a mixed quantum-classical framework, dubbed the moving Born-Oppenheimer approximation (MBOA), to describe the dynamics of slow degrees of freedom (DOFs) coupled to fast ones. As in the Born-Oppenheimer approximation (BOA), the fast degrees of freedom adiabatically follow a state that depends on the slow ones. Unlike the BOA, this state depends on both the positions and the momenta of the slow DOFs. We study several model systems: a spin-1/2 particle and a spinful molecule moving in a spatially inhomogeneous magnetic field, and a gas of fast particles coupled to a piston. The MBOA reveals rich dynamics for the slow degree of freedom, including reflection, dynamical trapping, and mass renormalization. It also significantly modifies the state of the fast DOFs. For example, the spins in the molecule are entangled and squeezed, while the gas of fast particles develops gradients that are synchronized with the motion of the piston for a long time. The MBOA can be used to describe both classical and quantum systems and has potential applications in quantum chemistry, correlated materials, atomic physics, molecular dynamics, and quantum sensing.

Comment on “A path integral over Hilbert space for quantum mechanics”

Annals of Physics · 2025-03-21

Incommensurate gapless ferromagnetism connecting competing symmetry-enriched deconfined quantum phase transitions

Physical review. B./Physical review. B · 2025-10-07 · 2 citations

We present a scenario in which a gapless extended phase serves as a “hub” connecting multiple symmetry-enriched deconfined quantum critical points. As a concrete example, we construct a lattice model with <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msubsup><a:mi mathvariant="double-struck">Z</a:mi><a:mn>2</a:mn><a:mspace width="0.16em"/></a:msubsup><a:mo>×</a:mo><a:msubsup><a:mi mathvariant="double-struck">Z</a:mi><a:mn>2</a:mn><a:mspace width="0.16em"/></a:msubsup><a:mo>×</a:mo><a:msubsup><a:mi mathvariant="double-struck">Z</a:mi><a:mn>2</a:mn><a:mspace width="0.16em"/></a:msubsup></a:mrow></a:math> symmetry for quantum spin-1/2 degrees of freedom that realizes four distinct gapful phases supporting antiferromagnetic long-range order and one extended incommensurate gapless ferromagnetic phase. The quantum phase transition between any two of the four gapped and antiferromagnetic phases goes through either a (deconfined) quantum critical point, a quantum tricritical point, or the incommensurate gapless ferromagnetic phase. In this phase diagram, it is possible to interpolate between four deconfined quantum critical points by passing through the extended gapless ferromagnetic phase. We identify the phases in the model and the nature of the transitions between them through a combination of analytical arguments and density matrix renormalization group studies.

Quantum Correction to the Orbital Hall Effect

Physical Review Letters · 2025-01-23 · 8 citations

Evaluations of the orbital Hall effect (OHE) have retained only interband matrix elements of the position operator. Here, we evaluate the OHE including all matrix elements of the position operator, including the technically challenging intraband elements. We recover previous results and find quantum corrections due to the noncommutativity of the position and velocity operators and interband matrix elements of the orbital angular momentum. The quantum corrections dominate the OHE responses of the topological antiferromagnet CuMnAs and of massive Dirac fermions.

Bose Metal in Atomically Thin NbSe2?

Journal Club for Condensed Matter Physics · 2025-02-28

Unveiling Resilient Superconducting Fluctuations in Atomically Thin NbSe2 through Higgs Mode Spectroscopy Authors: Yu Du, Gan Liu, Wei Ruan, Zhi Fang, Kenji Watanabe, Takashi Taniguchi, Ronghua Liu, Jian-Xin Li, and Xiaoxiang Xi Phys. Rev. Lett. 134, 066002 (2025) and supplemental material, DOI: 10.1103/PhysRevLett.134.066002 Recommended with a commentary by Daniel Arovas , University of California at […]

The two critical temperatures conundrum in La$_{1.83}$Sr$_{0.17}$CuO$_4$

SciPost Physics · 2024-06-05

The in-plane and out-of-plane superconducting stiffness of La_{1.83}Sr_{0.17}CuO_4 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>L</mml:mi> <mml:msub> <mml:mi>a</mml:mi> <mml:mn>1.83</mml:mn> </mml:msub> <mml:mi>S</mml:mi> <mml:msub> <mml:mi>r</mml:mi> <mml:mn>0.17</mml:mn> </mml:msub> <mml:mi>C</mml:mi> <mml:mi>u</mml:mi> <mml:msub> <mml:mi>O</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:mrow> </mml:math> rings appear to vanish at different transition temperatures, which contradicts thermodynamical expectation. In addition, we observe a surprisingly strong dependence of the out-of-plane stiffness transition on sample width. With evidence from Monte Carlo simulations, this effect is explained by very small ratio \alpha <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>α</mml:mi> </mml:math> of inter-plane over intra-plane Josephson couplings. For three dimensional rings of millimeter dimensions, a crossover from layered three dimensional to quasi one dimensional behavior occurs at temperatures near the thermodynamic transition temperature {T_{c}} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> , and the out-of-plane stiffness appears to vanish below {T_{c}} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> by a temperature shift of order \alpha L_a/{\xi^{\parallel}} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>α</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>a</mml:mi> </mml:msub> <mml:mi>/</mml:mi> <mml:msup> <mml:mi>ξ</mml:mi> <mml:mo>∥</mml:mo> </mml:msup> </mml:mrow> </mml:math> , where L_a/{\xi^{\parallel}} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>a</mml:mi> </mml:msub> <mml:mi>/</mml:mi> <mml:msup> <mml:mi>ξ</mml:mi> <mml:mo>∥</mml:mo> </mml:msup> </mml:mrow> </mml:math> is the sample’s width over coherence length. Including the effects of layer-correlated disorder, the measured temperature shifts can be fit by a value of \alpha=4.1× 10^{-5} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4.1</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , near {T_{c}} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> , which is significantly lower than its previously measured value near zero temperature.

Lieb-Schultz-Mattis Theorem for Open Quantum Systems

Journal Club for Condensed Matter Physics · 2024-02-29

1. Lieb-Schultz-Mattis Theorem in Open Quantum Systems Authors: Kohei Kawabata, Ramanjit Sohal, and Shinsei Ryu Phys. Rev. Lett. 132, 070402 (2024) and supplemental material DOI: 10.1103/PhysRevLett.132.070402 2. Reviving the Lieb–Schultz–Mattis Theorem in Open Quantum Systems Authors: Yi-Neng Zhou, Xingyu Li, Hui Zhai, Chengshu Li, and Yingfei Gu arXiv:2310.01475; DOI: 10.48550/arXiv.2310.01475 Recommended with a commentary by […]

Effects of non-integrability in a non-Hermitian time crystal

arXiv (Cornell University) · 2024-12-05

Time crystals are systems that spontaneously break time-translation symmetry, exhibiting repeating patterns in time. Recent work has shown that non-Hermitian Floquet systems can host a time crystalline phase with quasi-long-range order. In this work, we investigate the effect of introducing a non-integrable interaction term into this non-Hermitian time crystal model. Using a combination of numerical TEBD simulations, mean-field analysis, and perturbation theory, we find that the interaction term has two notable effects. First, it induces a shift in the phase diagram, moving the boundaries between different phases. Second, a sufficiently strong interaction induces an unexpected symmetry-breaking transition, which is not captured by the mean-field approach. Within average Hamiltonian theory, we trace this back to a ferromagnetic transition in the anisotropic non-Hermitian XXZ model. Our results demonstrate that the interplay between non-Hermitian dynamics and many-body interactions can lead to novel symmetry breaking.