The ${\rm LiHo_xY_{1-x}F_4}$ compound is widely considered to be the archetypal dipolar Quantum Ising system, with longitudinal dipolar interactions $V_{ij}^{zz}$ between ${\rm Ho}$ spins $\{i,j \}$ competing with transverse field-induced tunneling, to give a T=0 quantum phase transition. By varying the ${\rm Ho}$ concentration x, the typical strength $V_0$ of $V_{ij}^{zz}$ can be varied over many orders of magnitude; and so can the transverse field $H_{\perp}$. A new effective Hamiltonian is derived, starting from the electronuclear degrees of freedom, and valid at low and intermediate temperatures. For any such dipolar Quantum Ising system, the hyperfine interaction will dominate the physics at low temperatures, even if its strength $A_0 < V_0$: one must therefore go beyond an electronic transverse field Quantum Ising model. We derive the full phase diagram of this system, including all nuclear levels, as a function of transverse field $H_{\perp}$, temperature $T$, and dipole concentration x. For ${\rm LiHo_xY_{1-x}F_4}$ we predict a re-entrant critical field as a function of x. We also predict the phase diagram for x$=0.045$, and the behavior of the system in magnetic resonance and $μ$SR experiments.
Phase diagram with enhanced spin-glass region of mixed Ising / XY magnets LiHo$_{x}$Er$_{1-x}$F$_{4}$
本文给出了LiHo $_x$ Er $_{1-x}$ F $_4$（偶极耦合模型磁体的稀释系列）的实验相图，该相图是用交流磁化率和中子散射相结合的方法确定的。除了伊辛铁磁体LiHoF $_4$和XY反铁磁体LiErF $_4$之外，还确定了三个独特的相。在$x=0.86$下面，观察到嵌入的自旋玻璃相，其中自旋玻璃存在于铁磁结构内。在$x=0.57$下面观察到由冻结的针状团簇组成的Ising自旋玻璃。对于$x \sim 0.3 - 0.1$，出现反铁磁耦合的自旋玻璃。观察到的铁磁体的$T_C(x)$的减少不服从的平均场的预测，为LiHo $_x$ Y $_{1-x}$ F $_4$工作。
We present a systematic study of the phase diagram of LiHo$_x$Y$_{1-x}$F$_4$ ($0.25<x<1$) Ising ferromagnets obtained from neutron scattering measurements and mean-field calculations. We show that while the thermal phase transition decreases linearly with dilution, as predicted by mean-field theory, the critical transverse field at the quantum critical point is suppressed much faster. This behavior is related to competition between off-diagonal dipolar coupling and quantum fluctuations that are tuned by doping and applied field, respectively. In this paper, we quantify the deviation of the exp…
The rare-earth material $\mathrm{LiHoF_4}$ is believed to be an experimental realization of the celebrated (dipolar) Ising model, and upon the inclusion of a transverse field $B_x$, an archetypal quantum Ising model. Moreover, by substituting the magnetic Ho ions by non-magnetic Y ions, disorder can be introduced into the system giving rise to a dipolar disordered magnet and at high disorders to a spin-glass. Indeed, this material has been scrutinized experimentally, numerically and theoretically over many decades with the aim of understanding various collective magnetic phenomena. One of the …
Quantum annealing (QA) refers to an optimization process that uses quantum fluctuations to find the global minimum of a rugged energy landscape with many local minima. Conceptually, QA is often framed in the context of the disordered transverse field Ising model, in which a magnetic field applied perpendicular to the Ising axis tunes the quantum fluctuations and enables the system to tunnel through energy barriers, and hence reach the ground state more quickly. A solid state material closely related to this model, LiHo$_{0.45}$Y$_{0.55}$F$_4$, was shown to exhibit faster dynamics after a QA pr…
We derive an effective time independent Hamiltonian for the transverse Ising model coupled to a spin bath, in the presence of a high frequency AC magnetic field. We show that the spin blocking mechanism that removes the quantum phase transition can be suppressed by the AC field, allowing high tunability of the quantum critical point. Finally, we calculate the phase diagram within the RPA approximation for the case of spin $7/2$ nuclei, appropriate to the $LiHo_{x}Y_{1-x}F_{4}$ system.
Mesoscale patterns as observed, e.g., in ferromagnets, ferroelectrics, superconductors, mono-molecular films, or block-copolymers, reflect spatial variations of a pertinent order parameter at length- and time-scales that may be described classically. This raises the question for the relevance of mesoscale patterns near zero temperature phase transitions, also known as quantum phase transitions (QPTs). Here we report the magnetic susceptibility of LiHoF$_4$ -- a dipolar Ising ferromagnet -- near a well-understood transverse-field quantum critical point (TF-QCP). When tilting the magnetic field …
We present direct local-probe evidence for strongly hybridized nuclear-electronic spin states of an Ising ferromagnet LiHoF$_4$ in a transverse magnetic field. The nuclear-electronic states are addressed via a magnetic resonance in the GHz frequency range using coplanar resonators and a vector network analyzer. The magnetic resonance spectrum is successfully traced over the entire field-temperature phase diagram, which is remarkably well reproduced by mean-field calculations. Our method can be directly applied to a broad class of materials containing rare-earth ions for probing the substantial…
The interplay between quantum fluctuations and disorder is investigated in a spin-glass model, in the presence of a uniform transverse field $Γ$, and a longitudinal random field following a Gaussian distribution with width $Δ$. The model is studied through the replica formalism. This study is motivated by experimental investigations on the LiHo$_x$Y$_{1-x}$F$_4$ compound, where the application of a transverse magnetic field yields rather intriguing effects, particularly related to the behavior of the nonlinear magnetic susceptibility $χ_3$, which have led to a considerable experimental and the…
We study the effect of coupling a spin bath environment to a system which, at low energies, can be modeled as a quantum Ising system. A field theoretic formalism incorporating both thermal and quantum fluctuations is developed to derive results for the thermodynamic properties and response functions, both for a toy model and for the $LiHoF_4$ system, in which spin-8 electronic spins couple to a spin-$7/2$ nuclear spin bath: the phase transition then occurs in a system of electronuclear degrees of freedom, coupled by long-range dipolar interactions. The quantum Ising phase transition still exis…
We present the design of a compact AC susceptometer for studies under arbitrarily oriented static magnetic fields, in particular magnetic fields oriented transverse to the AC excitation field. The small size of the susceptometer permits versatile use in conventional cryostats with superconducting magnet systems. The design of the susceptometer minimizes parasitic signal contributions while providing excellent thermal anchoring suitable for measurements in a wide range down to very low temperatures. The performance is illustrated by means of measurements of the transverse susceptibility at the …
The Harper equation arising out of a tight-binding model of electrons on a honeycomb lattice subject to a uniform magnetic field perpendicular to the plane is studied. Contrasting and complementary approaches involving von Neumann entropy, fidelity, fidelity susceptibility, multifractal analysis are employed to characterize the phase diagram. The phase diagram consists of three phases: two metallic phases and an insulating phase. A variant model where next nearest neighbor hopping is included, exhibits a mobility edge and does not allow for a simple single phase diagram characterizing all the …
We present a systematic study of the crystal field interactions in the Li$R$F$_4$, $R$ = Gd, Ho, Er, Tm and Yb, family of rare-earth magnets. Using detailed inelastic neutron scattering measurements we have been able to quantify the transition energies and wavefunctions for each system. This allows us to quantitatively describe the high-temperature susceptibility measurements for the series of materials and make predictions based on a mean-field approach for the low-temperature thermal and quantum phase transitions. We show that coupling between crystal field and phonon states leads to linesha…
Motivated by the complex phase diagram of MnWO4, we investigate competition between anisotropy, magnetic field, and helicity for the anisotropic next-nearest-neighbor Heisenberg model. Apart from two competing exchanges, which favor a spiral magnetic structure, the model features the bi-axial single-ion anisotropy. The model is treated in the real-space mean-field approximation and the phase diagram containing various incommensurate and commensurate states is obtained for different field orientations. We discuss similarities and differences of the theoretical phase diagram and the experimental…
We study the phase diagram of an extended parafermion chain, which, in addition to terms coupling parafermions on neighbouring sites, also possesses terms involving four sites. Via a Fradkin--Kadanoff transformation the parafermion chain is shown to be equivalent to the non-chiral $\mathbb{Z}_3$ axial next-nearest neighbour Potts model. We discuss a possible experimental realisation using hetero-nanostructures. The phase diagram contains several gapped phases, including a topological phase where the system possesses three (nearly) degenerate ground states, and a gapless Luttinger-liquid phase.
We investigate the phase diagram of two-dimensional (2D) Hubbard model by employing the optimization variational Monte Carlo method. The 2D Hubbard model is the most simple electronic model for cuprate high-temperature superconductors. The phase diagram consists of three regions; they are antiferromagnetic insulator (AFI) region, superconducting (SC) region and the coexistent region of superconductivity and antiferromgantism. The phase diagram obtained by numerical calculations well agrees with the experimental phase diagram for high-temperature cuprates. We mainly focused on the effect of $t'…
Comparison of the phase diagram of the half-filled layered organic superconductors with the phase diagram of the RVB theory of the Hubbard-Heisenberg model
We consider the phase diagram of a ferromagnetic system driven to a quantum phase transition with a tuning parameter $p$. Before being suppressed, the transition becomes of the first order at a tricritical point, from which wings emerge under application of the magnetic field $H$ in the $T$-$p$-$H$ phase diagram. We show that the edge of the wings merge with tangent slopes at the tricritical point.
We study a tight binding model of $\mathbb{Z}_3$-Fock parafermions with single-particle and pair-hopping terms. The phase diagram has four different phases: a gapped phase, a gapless phase with central charge $c=2$, and two gapless phases with central charge $c=1$. We characterise each phase by analysing the energy gap, entanglement entropy and different correlation functions. The numerical simulations are complemented by analytical arguments.
We study how to engineer holographic models with features of a high temperature superconductor phase diagram. We introduce a field in the bulk which provides a tunable "doping" parameter in the boundary theory. By designing how this field changes the effective masses of other order parameter fields, desired phase diagrams can be engineered. We give examples of generating phase diagrams with phase boundaries similar to a superconducting dome and an anti-ferromagnetic phase by including two order parameter fields. We also explore whether the pseudo gap phase can be described without adding anoth…
