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Register a new userLow Temperature Domain Wall Freezing and Non-Equilibrium Dynamics in the Transverse-Field Ising Model Material CoNb$_2$O$_6$
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CoNb$_2$O$_6$ is a rare realization of the transverse field Ising model (TFIM), making it a useful tool for studying both equilibrium and non-equilibrium many-body quantum physics. Despite a large body of work dedicated to characterizing this material, details of the ordered states in the presence of relatively weak transverse fields have not been discussed in detail. Here, we present a detailed study of CoNb$_2$O$_6$ via ac susceptibility measurements in order to further characterize its low temperature behavior in the presence of a transverse field. Specifically, we call attention to an unconventional freezing transition in zero-field below T$_F$ = 1.2~K, occurring emph{within} the well-known commensurate antiferromagnetic (CAFM) state that onsets at $T_{N2}$ = 1.9~K. We performed a series of transverse-field quenches into this frozen state, which resulted in a slowly relaxing susceptibility, $chi^{prime}(t)$, that followed a logarithmic decay within the time range measured. We discuss the frozen state in the context of the freezing of previously discussed free chains arising from domain walls between the four degenerate sublattices of the CAFM state. We also attempted to observe Kibble-Zurek scaling by quenching the transverse field into the frozen state at different rates. This produced a null result; the behavior can be fully explained by coarsening of domains over the timescale of the quenches. The absence of a clear Kibble-Zurek scaling is itself surprising, given the proposed ubiquity of the phenomenon for general second order phase transitions.
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We present experimental and theoretical evidence that an interesting quantum many-body effect -- quasi-particle breakdown -- occurs in the quasi-one-dimensional spin-1/2 Ising-like ferromagnet CoNb$_2$O$_6$ in its paramagnetic phase at high transverse field as a result of explicit breaking of spin inversion symmetry. We propose a quantum spin Hamiltonian capturing the essential one-dimensional physics of CoNb$_2$O$_6$ and determine the exchange parameters of this model by fitting the calculated single particle dispersion to the one observed experimentally in applied transverse magnetic fields. We present high-resolution inelastic neutron scattering measurements of the single particle dispersion which observe anomalous broadening effects over a narrow energy range at intermediate energies. We propose that this effect originates from the decay of the one particle mode into two-particle states. This decay arises from (i) a finite overlap between the one-particle dispersion and the two-particle continuum in a narrow energy-momentum range and (ii) a small misalignment of the applied field away from the direction perpendicular to the Ising axis in the experiments, which allows for non-zero matrix elements for decay by breaking the $mathbb{Z}_2$ spin inversion symmetry of the Hamiltonian.
Kink bound states in the one dimensional ferromagnetic Ising chain compound CoNb$_2$O$_6$ have been studied using high resolution time-domain terahertz spectroscopy in zero applied magnetic field. When magnetic order develops at low temperature, nine bound states of kinks become visible. Their energies can be modeled exceedingly well by the Airy function solutions to a 1D Schrodinger equation with a linear confining potential. This sequence of bound states terminates at a threshold energy near two times the energy of the lowest bound state. Above this energy scale we observe a broad feature consistent with the onset of the two particle continuum. At energies just below this threshold we observe a prominent excitation that we interpret as a novel bound state of bound states -- two pairs of kinks on neighboring chains.
Close to the quantum critical point of the transverse-field Ising spin-chain model, an exotic dynamic spectrum was predicted to emerge upon a perturbative longitudinal field. The dynamic spectrum consists of eight particles and is governed by the symmetry of the $E_8$ Lie algebra. Here we report on high-resolution terahertz spectroscopy of quantum spin dynamics in the ferromagnetic Ising-chain material CoNb$_2$O$_6$. At 0.25 K in the magnetically ordered phase we identify characteristics of the first six $E_8$ particles, $mathbf{m}_1$ to $mathbf{m}_6$, and the two-particle ($mathbf{m}_1+mathbf{m}_2$) continuum in an applied transverse magnetic field of $B_c^{1D}=4.75$ T, before the three-dimensional magnetic order is suppressed above $B_c^{3D}approx 5.3$ T. The observation of the higher-energy particles ($mathbf{m}_3$ to $mathbf{m}_6$) above the low-energy two-particle continua features quantum many-body effects in the exotic dynamic spectrum.
We investigate the inverse freezing in the fermionic Ising spin-glass (FISG) model in a transverse field $Gamma$. The grand canonical potential is calculated in the static approximation, replica symmetry and one-step replica symmetry breaking Parisi scheme. It is argued that the average occupation per site $n$ is strongly affected by $Gamma$. As consequence, the boundary phase is modified and, therefore, the reentrance associated with the inverse freezing is modified too.
The quantum Kibble-Zurek mechanism (QKZM) predicts universal dynamical behavior in the vicinity of quantum phase transitions (QPTs). It is now well understood for one-dimensional quantum matter. Higher-dimensional systems, however, remain a challenge, complicated by fundamental differences of the associated QPTs and their underlying conformal field theories. In this work, we take the first steps towards exploring the QKZM in two dimensions. We study the dynamical crossing of the QPT in the paradigmatic Ising model by a joint effort of modern state-of-the-art numerical methods. As a central result, we quantify universal QKZM behavior close to the QPT. However, upon traversing further into the ferromagnetic regime, we observe deviations from the QKZM prediction. We explain the observed behavior by proposing an {it extended QKZM} taking into account spectral information as well as phase ordering. Our work provides a starting point towards the exploration of dynamical universality in higher-dimensional quantum matter.
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