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arXiv:1202.4958 · New Journal of Physics

Quantum criticality at high temperature revealed by spin echo

Shao-Wen Chen, Zhan-Feng Jiang, Ren-Bao Liu

Published Apr 18, 2013• 17 citations
arXivHTMLPDF

Abstract

Quantum criticality occurs when the ground state of a macroscopic quantum system changes abruptly on tuning system parameters. It is an important indicator of new quantum matters emerging. In conventional methods, quantum criticality is observable only at zero or low temperature (as compared with the interaction strength in the system). We find that a quantum probe, if its coherence time is long, can detect the quantum criticality of a system at high temperature. In particular, the echo control over a spin probe can remove the thermal fluctuation effects and hence reveal the critical quantum fluctuation without requiring low temperature. We first use the exact solution of the one-dimensional transverse-field Ising model to demonstrate the possibility of detecting the quantum criticality at high temperature by spin echo. The critical behaviors were calculated using the exact solution and understood by the noise spectrum analysis in the Gaussian noise approximation. By numerical simulation, we further verify that the high-temperature quantum criticality also exists in the probe coherence measurement of spin systems with dipolar couplings. Using the noise spectrum analysis, we establish the correspondence between the necessary low temperature ( T QC ) in conventional methods and the necessary long coherence time ( t QC ) in probe decoherence measurement to observe the quantum criticality, that is, T QC ∼ 1/ t QC and much less than the interaction strength of the system. For example, probes with quantum coherence times of milliseconds or seconds can be used to study, without cooling the system, quantum criticality that was previously known to be only observable at extremely low temperatures of nano- or pico-kelvin. This finding provides a new possibility to study quantum matters.

DOI
10.1088/1367-2630/15/4/043032

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Quantum criticality occurs when the ground state of a macroscopic quantum system changes abruptly on tuning system parameters. It is an important indicator of new quantum matters emerging. In conventional methods, quantum criticality is observable only at zero or low temperature (as compared with the interaction strength in the system). We find that a quantum probe, if its coherence time is long, can detect the quantum criticality of a system at high temperature. In particular, the echo control over a spin probe can remove the thermal fluctuation effects and hence reveal the critical quantum fluctuation without requiring low temperature. We first use the exact solution of the one-dimensional transverse-field Ising model to demonstrate the possibility of detecting the quantum criticality at high temperature by spin echo. The critical behaviors were calculated using the exact solution and understood by the noise spectrum analysis in the Gaussian noise approximation. By numerical simulation, we further verify that the high-temperature quantum criticality also exists in the probe coherence measurement of spin systems with dipolar couplings. Using the noise spectrum analysis, we establish the correspondence between the necessary low temperature ( T QC ) in conventional methods and the necessary long coherence time ( t QC ) in probe decoherence measurement to observe the quantum criticality, that is, T QC ∼ 1/ t QC and much less than the interaction strength of the system. For example, probes with quantum coherence times of milliseconds or seconds can be used to study, without cooling the system, quantum criticality that was previously known to be only observable at extremely low temperatures of nano- or pico-kelvin. This finding provides a new possibility to study quantum matters.
Quantum criticality, being important as an indicator of new quantum matters emerging, is known to occur only at zero or low temperature. We find that a quantum probe, if its coherence time is long, can detect quantum criticality at infinitely high temperature. In particular, the echo control over a spin probe can remove the thermal fluctuation effects and hence reveals the quantum fluctuation effects. Probes with quantum coherence time of milliseconds or seconds can be used to study emerging quantum orders that would occur at extremely low temperatures of nano- or pico-Kelvin. This discovery establishes a physical link between time and inverse temperature and provides a new route to the wonderland of quantum matters.
Using spin-echo nuclear magnetic resonance in the model transverse field Ising system TmVO_{4}, we show that low frequency quantum fluctuations at the quantum critical point have a very different effect on ^{51}V nuclear spins than classical low-frequency noise or fluctuations that arise at a finite temperature critical point. Spin echoes filter out the low-frequency classical noise but not the quantum fluctuations. This allows us to directly visualize the quantum critical fan and demonstrate the persistence of quantum fluctuations at the critical coupling strength in TmVO_{4} to high temperatures in an experiment that remains transparent to finite temperature classical phase transitions. These results show that while dynamical decoupling schemes can be quite effective in eliminating classical noise in a qubit, a quantum critical environment may lead to rapid entanglement and decoherence.
We face the problem of detecting and featuring footprints of quantum criticality in the finite-temperature behavior of quantum many-body systems. Our strategy is that of comparing the phase diagram of a system displaying a T=0T=0T=0 quantum phase transition with that of its classical limit, in order to single out the genuinely quantum effects. To this aim, we consider the one-dimensional Ising model in a transverse field: while the quantum S=1∕2S=1∕2S=1∕2 Ising chain is exactly solvable and extensively studied, results for the classical limit $(S\ensuremath{\rightarrow}\ensuremath{\infty})$ of such model are lacking, and we supply them here. They are obtained numerically, via the transfer-matrix method, and their asymptotic low-temperature behavior is also derived analytically by self-consistent spin-wave theory. We draw the classical phase diagram according to the same procedure followed in the quantum analysis, and the two phase diagrams are found unexpectedly similar: Three regimes are detected also in the classical case, each characterized by a functional dependence of the correlation length on temperature and field analogous to that of the quantum model. What discriminates the classical from the quantum case are the different values of the exponents entering such dependencies, a consequence of the different nature of zero-temperature quantum fluctuations with respect to the thermal ones.
Conventional wisdom dictates that quantum effects become unimportant at high temperatures. In magnets, when the thermal energy exceeds interactions between atomic magnetic moments, the moments are usually uncorrelated, and classical paramagnetic behavior is observed. This thermal decoherence of quantum spin behaviors is a major hindrance to quantum information applications of spin systems. Remarkably, our neutron scattering experiments on Yb chains in an insulating perovskite crystal defy these conventional expectations. We find a sharply defined spectrum of spinons, fractional quantum excitations of spin-1/2 chains, to persist to temperatures much higher than the scale of the interactions between Yb magnetic moments. The observed sharpness of the spinon continuum’s dispersive upper boundary indicates a spinon mean free path exceeding ≈ 35 inter-atomic spacings at temperatures more than an order of magnitude above the interaction energy scale. We thus discover an important and highly unique quantum behavior, which expands the realm of quantumness to high temperatures where entropy-governed classical behaviors were previously believed to dominate. Our results have profound implications for spin systems in quantum information applications operating at finite temperatures and motivate new developments in quantum metrology. Thermal excitations are typically detrimental to quantum coherence. Here, using inelastic neutron scattering measurements, the authors observe a sharp spinon spectrum in the spin-1/2 chain compound YbAlO3 at temperatures well above the energy scale of spin interactions, indicating long-range quantum coherence.
Phase transitions occur when a macroscopic number of local degrees of freedom coherently change their behavior. In ground states of quantum many-body systems, phase transitions due to quantum fluctuations are observed as non-analytic behaviors of order parameters, such as magnetization, as functions of a conjugate parameter, such as the magnetic field. However, as soon as thermal fluctuations are present, these effects are believed to disappear for local observables. We show that this is not necessarily the case: order parameters may still show non-analytic behaviors within their dynamics. With the example of the Ising model and using methods based on hydrodynamic fluctuations, we evaluate the exact order-parameter correlation time, in space-time directions of all velocities, in equilibrium states at nonzero temperature. We reveal non-analytic behaviors of spin correlation times as functions of the magnetic field, velocity, and temperature. As a function of the magnetic field, they occur at values that continuously approach that of the zero-temperature equilibrium transition point as the velocity is decreased and reach it within the light cone, where we obtain a new, temperature-independent logarithmic divergence characterizing the collective dynamics. Thus, collective effects induced by quantum fluctuations persist within the dynamics of local observables.
Quantum phase transitions take place between distinct phases of matter at zero temperature. Near the transition point, exotic quantum symmetries can emerge that govern the excitation spectrum of the system. A symmetry described by the E8 Lie group with a spectrum of eight particles was long predicted to appear near the critical point of an Ising chain. We realize this system experimentally by using strong transverse magnetic fields to tune the quasi-one-dimensional Ising ferromagnet CoNb2O6 (cobalt niobate) through its critical point. Spin excitations are observed to change character from pairs of kinks in the ordered phase to spin-flips in the paramagnetic phase. Just below the critical field, the spin dynamics shows a fine structure with two sharp modes at low energies, in a ratio that approaches the golden mean predicted for the first two meson particles of the E8 spectrum. Our results demonstrate the power of symmetry to describe complex quantum behaviors.