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arXiv:2601.20926

Quench spectroscopy of amplitude modes in a one-dimensional critical phase

Hyunsoo Ha, David A. Huse, Rhine Samajdar

cond-mat.str-elcond-mat.quant-gascond-mat.stat-mechquant-phSubmitted Jan 28, 2026• Announced Jan 30, 2026• 0 citations
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Abstract

We investigate the emergence of an amplitude (Higgs-like) mode in the gapless phase of the $(1+1)$D XXZ spin chain. Unlike conventional settings where amplitude modes arise from spontaneous symmetry breaking, here, we identify a symmetry-preserving underdamped excitation on top of a Luttinger-liquid ground state. Using nonequilibrium quench spectroscopy, we demonstrate that this mode manifests as oscillations of U(1)-symmetric observables following a sudden quench. By combining numerical simulations with Bethe-ansatz analyses, we trace its microscopic origin to specific families of string excitations. We further discuss experimental pathways to detect this mode in easy-plane quantum magnets and programmable quantum simulators. Our results showcase the utility of quantum quenches as a powerful tool to probe collective excitations, beyond the scope of linear response.

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7+16 pages, 3+5 figures

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We investigate the emergence of an amplitude (Higgs-like) mode in the gapless phase of the (1+1)(1+1)(1+1)D XXZ spin chain. Unlike conventional settings where amplitude modes arise from spontaneous symmetry breaking, here, we identify a symmetry-preserving underdamped excitation on top of a Luttinger-liquid ground state. Using nonequilibrium quench spectroscopy, we demonstrate that this mode manifests as oscillations of U(1)-symmetric observables following a sudden quench. By combining numerical simulations with Bethe-ansatz analyses, we trace its microscopic origin to specific families of string excitations. We further discuss experimental pathways to detect this mode in easy-plane quantum magnets and programmable quantum simulators. Our results showcase the utility of quantum quenches as a powerful tool to probe collective excitations, beyond the scope of linear response.
We compute the dynamics of localized excitations produced by a quantum quench in the spin-1/2 XXZ chain. Using numerics combining the density-matrix renormalization group and exact time evolution, as well as analytical arguments, we show that fractionalization due to interactions in the prequench state gives rise to ``ultrarelativistic'' density waves that travel at the maximum band velocity. The system is initially prepared in the ground state of the chain within the gapless XYXYXY phase, which admits a Luttinger liquid (LL) description at low energies and long wavelengths. The Hamiltonian is then suddenly quenched to a band insulator, after which the chain evolves unitarily. Through the gapped dispersion of the insulator spectrum, the postquench dynamics serve as a ``velocity microscope,'' revealing initial-state particle correlations via space-time density propagation. We show that the ultrarelativistic wave production is tied to the particular way in which fractionalization evades Pauli blocking in the zero-temperature initial LL state.
We investigate the amplitude (Higgs) mode associated with longitudinal fluctuations of the order parameter at the continuous spontaneous symmetry breaking phase transition. In quantum magnets, due to the fast decay of the amplitude mode into low-energy Goldstone excitations, direct observation of this mode represents a challenging task. By focusing on a quasi-one-dimensional geometry, we circumvent the difficulty and investigate the amplitude mode in a system of weakly coupled spin chains with the help of quantum Monte Carlo simulations, stochastic analytic continuation, and a chain-mean field approach combined with a mapping to the field-theoretic sine-Gordon model. The amplitude mode is observed to emerge in the longitudinal spin susceptibility in the presence of a weak symmetry-breaking staggered field. A conventional measure of the amplitude mode in higher dimensions, the singlet bond mode, is found to appear at a lower than the amplitude mode frequency. We identify these two excitations with the second (first) breather of the sine-Gordon theory, correspondingly. In contrast to higher-dimensional systems, the amplitude and bond order fluctuations are found to carry significant spectral weight in the quasi-1D limit.
Spontaneous symmetry breaking occurs in a physical system whenever the ground state does not share the symmetry of the underlying theory, e.g., the Hamiltonian. This mechanism gives rise to massless Nambu-Goldstone modes and massive Anderson-Higgs modes. These modes provide a fundamental understanding of matter in the Universe and appear as collective phase or amplitude excitations of an order parameter in a many-body system. The amplitude excitation plays a crucial role in determining the critical exponents governing universal nonequilibrium dynamics in the Kibble-Zurek mechanism (KZM). Here, we characterize the amplitude excitations in a spin-1 condensate and measure the energy gap for different phases of the quantum phase transition. At the quantum critical point of the transition, finite-size effects lead to a nonzero gap. Our measurements are consistent with this prediction, and furthermore, we demonstrate an adiabatic quench through the phase transition, which is forbidden at the mean field level. This work paves the way toward generating entanglement through an adiabatic phase transition.
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The elementary excitation spectrum of a many-body quantum system encodes many key properties, including phenomena as diverse as transport, thermalisation and ground state structure. Excitation spectra of strongly correlated systems are typically encoded in dynamical structure factors, which are demanding to measure experimentally and challenging to compute classically. Here we use quench spectroscopy on a superconducting quantum processor to extract excitation spectra of spin chains of L=101L=101L=101 spins. By tailoring the combination of quench protocol and observable, we selectively access distinct excitation sectors across several phases of the spin-1/21/21/2 XXZ chain, resolving free magnons, multi-magnon bound states, and two-spinon continua. Notably, we demonstrate that the protocol does not rely on ground state preparation: in the classically challenging gapless regime, we extract spectra directly from the quench dynamics of easily prepared product states, a procedure that is natural and straightforward on quantum hardware. Our work establishes quench spectroscopy as a fast and flexible probe of many-body excitation spectra on digital quantum hardware, introduces a novel quench protocol that does not require costly state preparation routines, and provides a scalable route towards regimes where classical simulation may become intractable.
Symmetry-breaking phase transitions are central to our understanding of states of matter. When a continuous symmetry is spontaneously broken, new excitations appear that are tied to fluctuations of the order parameter. In superconductors and fermionic superfluids, the phase and amplitude can fluctuate independently, giving rise to two distinct collective branches. However, amplitude fluctuations are difficult to both generate and measure, as they do not couple directly to the density of fermions and have only been observed indirectly to date. Here, we excite amplitude oscillations in an atomic Fermi gas with resonant interactions by an interaction quench. Exploiting the sensitivity of Bragg spectroscopy to the amplitude of the order parameter, we measure the time-resolved response of the atom cloud, directly revealing amplitude oscillations at twice the frequency of the gap. The magnitude of the oscillatory response shows a strong temperature dependence, and the oscillations appear to decay faster than predicted by time-dependent Bardeen-Cooper-Schrieffer theory applied to our experimental setup.