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.
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.
The concept of T = 0 quantum phase transi-tions has emerged as an overarching theme in strongly correlated electron physics [1–9]. The nature of quantum fluctuations near the quantum critical point, however, remains enigmatic [10]. How well does the quantum criticality account for finite temperature properties? How high in tem-perature does the effect of the quantum critical point persist?[10, 11] The dearth of appropriate model materials has not permitted experimental-ists to address these fundamental questions even for the transverse field Ising chain (TFIC), a cel-ebrated textbook example of quantum criticality [6]. Here we use NMR (Nuclear Magnetic Res-onance) to map the evolution of quantum spin fluctuations in CoNb2O6 [12–14], which has re-cently been proposed as an ideal model material for the TFIC [15, 16]. We will demonstrate that the effect of the quantum critical point persists to a remarkably high temperature, T ∼ 0.4J, where the exchange coupling J is the only energy scale in the problem.
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.
The quantum Ising model is perhaps the simplest possible model of a quantum magnetic material. Despite its simplicity, its versatility and wide range of applications, from quantum computation, to combinatorial optimization, to biophysics, make it one of the most important models of modern physics. In this thesis, we develop a general framework for studying quantum Ising systems with an arbitrary single ion Hamiltonian, with emphasis on the effects of quantum fluctuations, and the quantum phase transition between paramagnetic and ferromagnetic states that occurs when a magnetic field is applied transverse to the easy axis of the system. The magnetic insulating crystal LiHoF₄ is a physical realization of the quantum Ising model, with the additional features that the dominant coupling between spins is the long range dipolar interaction, and each electronic spin is strongly coupled to a nuclear degree of freedom. These nuclear degrees of freedom constitute a spin bath environment acting on the system. In this thesis, we present an effective low temperature Hamiltonian for LiHoF₄ that incorporates both these features, and we analyze the effects of the nuclear spin bath on the system. We find the lowest energy crystal field excitation in the system is gapped at the quantum critical point by the presence of the nuclear spins, with spectral weight being transferred down to a lower energy electronuclear mode that fully softens to zero at the quantum critical point. Furthermore, we present a toy model, the spin half spin half model, that illustrates the effects of an anisotropic hyperfine interaction on a quantum Ising system. We find the critical transverse field is increased when the longitudinal hyperfine coupling is dominant, as well as an enhancement of both the longitudinal electronic susceptibility and an applied longitudinal field. In addition, we present a field theoretic formalism for incorporating the effects of fluctuations beyond the random phase approximation in general quantum Ising systems. We find that any regular on site interaction, such as a nuclear spin bath, does not fundamentally alter the critical properties of a quantum Ising system. This formalism is used to calculate corrections to the magnetization of LiHoF₄.
The transverse field Ising chain model is ideally suited for testing the fundamental ideas of quantum phase transitions because its well-known T ¼ 0 ground state can be extrapolated to finite temperatures.Nonetheless, the lack of appropriate model materials hindered the past effort to test the theoretical predictions.Here, we map the evolution of quantum fluctuations in the transverse field Ising chain based on nuclear magnetic resonance measurements of CoNb 2 O 6 , and we demonstrate the finite-temperature effects on quantum criticality for the first time.From the temperature dependence of the 93 Nb longitudinal relaxation rate 1=T 1 , we identify the renormalized classical, quantum critical, and quantum disordered scaling regimes in the temperature (T) vs transverse magnetic field (h ⊥ ) phase diagram.Precisely at the critical field h c ⊥ ¼ 5.25 Æ 0.15 T, we observe a power-law behavior, 1=T 1 ∼ T -3=4 , as predicted by quantum critical scaling.Our parameter-free comparison between the data and theory reveals that quantum fluctuations persist up to as high as T ∼ 0.4J, where the intrachain exchange interaction J is the only energy scale of the problem.
For a system at absolute zero temperature, all thermal fluctuations are frozen out, while quantum fluctuations prevail.These microscopic quantum fluctuations can induce a quantum phase transition (QPT) in the ground state of a many-body system when the relative strength of two competing energy terms is varied across a critical value.This paper presents a detailed and quantitative study of the magnetic properties of Ising two-spin system at zero temperature in the presence of longitudinal, transverse and mixed fields, and also at finite temperatures.At the critical longitudinal magnetic field, the system is found to undergo a QPT to a ferromagnetic state.For this system, an infinitesimal departure from zero transverse field is found to trigger off QPT and also remove the degeneracies that persisted even in the presence of longitudinal field.These quantum fluctuations, leading to QPT are more evident in the mixed field than the separate effect of longitudinal and transverse fields.The observed quantum effects at zero temperature for this system are found to be completely wiped out at finite temperatures due to thermal fluctuations.A temperature increase favours antiferromagnetic alignment of spins, while a decrease in temperature favours ferromagnetic alignment.
A comprehensive comparison between the magnetic field- and temperature-dependent low-frequency spin dynamics in the antiferromagnetic spin-1/2 Heisenberg chain system copper pyrazine dinitrate, probed via the 13C nuclear magnetic resonance relaxation rate ${T}_{1}^{\ensuremath{-}1}$, and the field theoretical approach in the Luttinger liquid regime was performed. We found very good agreement between experiment and theory in the investigated temperature and field range. Our results demonstrate how spin-spin interactions strongly affect the spin dynamics of Heisenberg spin chain compounds in the vicinity of the quantum critical point.