Session Y64: Quantum Phase Transitions and Quantum Monte Carlo Simulations

Geotherm tracks the quantum critical regime of FeO: an eDMFT study

A potentially key contributor to compositions and processes at Earth’s core-mantle boundary, FeO has demonstrated over the past several decades an astonishing variety of conductive, magnetic, and structural phases, depending on local pressure (P) and temperature (T) conditions. What presently remains to be well understood is the physical picture underlying this unconventional behavior and its geophysical implications. Here, we seek to rectify this deficiency by analyzing (B1-type) FeO’s electronic structure across its (P,T) phase diagram, through large scale theoretical modeling, using state-of-the-art “embedded dynamical mean-field theory” (eDMFT). We establish that FeO’s phase diagram comprises 3 distinct regions, which emerge around the Mott point and possess unique transport trends. Of these, we find that (P,T) conditions which are largely relevant for FeO in geophysics occupy precisely the intermediate quantum critical regime, a wide finite-temperature region separating the metallic and the insulating phases of matter. Quantum critical transport found here displays weak P/T dependence and moderate electrical resistance around the Mott-Ioffe-Regel limit, which is dominated by strong electron-electron scattering.   

Probing cluster dynamics in Ni-Cr alloys close to the ferromagnetic quantum critical point by μSR

Ferromagnetic alloys exhibit a quantum critical point (QCP) driven by disorder accompanied by a quantum Griffiths phase (QGP), a region of dynamic clusters. This has been previously studied in Ni_1-xV_x alloys around a critical concentration x_c with muon spin relaxation (μSR) measurements [1] supporting the signatures of a QGP. Ni_1-xCr_x alloys should show similar phenomenology but with significantly smaller nuclear magnetic moments that mean muons are able to probe even smaller electronic magnetic fields. Muon measurements on two polycrystalline samples of Ni_1-xCr_x alloys close to x_c have been performed using the MuSR instrument at ISIS. Ni_0.88Cr_0.12 muon data show a broad static magnetic field distribution indicating an ordered ferromagnetic state and signs of coexisting dynamic clusters below 2.5K. The presence of long-range ferromagnetic order with short-range fluctuations is similar to Ni_0.89V_0.11 confirmed by μSR [1] and small-angle neutron scattering measurements [2]. For Ni_0.873Cr_0.127, the muon data defy simple descriptions indicating more complex inhomogeneities in space and multiple timescales and suggest a cluster glass toward low temperatures.

[1] R. Wang et al.  Phys. Rev. Lett. 118, 267202 (2017)

[2] A. Schroeder et al. AIP Advances 10, 015036 (2020)   

Quantum phase transitions and finite entanglement scaling

The density matrix renormalization group provides a powerful tool in the numerical study of 1D systems by finding matrix product state (MPS) approximations to the ground states. Its efficiency is underpinned by the low area-law entanglement of the ground states of gapped 1D systems. The area law of entanglement is famously violated at quantum critical points (QCP) where the gap closes and the behavior of the entanglement entropy is logarithmic. Because of this MPSs fail to capture important features of critical states such as the diverging correlation length. Yet it was conjectured that the effect of finite bond dimension of the MPS is characterized by a single length scale that is determined by the conformal field theory description of the QCP, this conjecture is known as the finite entanglement scaling. In our work, we provide a more detailed picture of the structure of the MPS approximations to the states at and near critical points beyond the scaling of the correlation length, in particular showing how the phase transitions become discontinuous. The analysis is based on analytical calculations for integrable spin chains and confirmed numerically.   

Localization of the Higgs mode at the superfluid-Mott glass quantum phase transition

We study the effects of disorder on the collective excitations near the superfluid-Mott glass quantum phase transition in a system of disordered bosons. Via large-scale Monte Carlo methods, we calculate relevant dynamical susceptibilities to study the Higgs (amplitude) and goldstone (phase) modes of the order parameter across the quantum critical point. We show that the introduction of disorder localizes the Higgs mode in the superfluid phase in both two and three spatial dimensions. We explore experimental ramifications of the effects of disorder on these modes and discuss the broader implications of unconventional dynamics in disordered quantum phase transitions.   

Probing the nematic insulator Tm1-xYxVO4 with neutron scattering near quantum criticality

The insulator TmVO₄ have recently been established as a model system to study electronic nematicity near quantum criticality. The material undergoes a continuous ferroquadrupolar transition due to partially filled 4f orbitals of the Tm ions, mediated by long range interactions via the lattice. The transition can be described by the magnetic transverse field Ising model with a crossover to the nematic transverse field Ising model near the quantum critical region. Here we present results from neutron scattering on single crystal and powder samples of the system Tm_1-xY_xVO₄ at various compositions in order to study the effects of disorder on electronic nematicity near a quantum critical point.   

Direct Observation of Collective Electronuclear Modes About a Quantum Critical Point

The quantum Ising magnet LiHoF₄ provides an ideal platform for exploring excitations near a quantum phase transition. We use microwave spectroscopy to probe the dynamics near the critical point, finding that instead of a single electronic mode we observe a sequence of low energy modes in which the spin-1/2 Ising electronic spins hybridize with the spin-7/2 ¹⁶⁵Ho nuclei. The lowest-lying electronuclear mode softens at the approach to the quantum critical point, showing that quantum criticality persists in the presence of disorder. As expected, a magnetic field applied parallel to the Ising axis rapidly quenches the mode softening. We also observe spectroscopic features that provide insight into the domain formation and dynamics, as well as the physics of strong coupling between the electronuclear excitations and microwave resonator photons. The electronuclear modes observed here and in related solid-state materials, and their coupling to the environment, should be of interest in microwave-optical transduction.   

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Quantum criticality is thought to underlie many fascinating phenomena in highly-correlated electron systems, including non-Fermi liquid phenomenology. Furthermore, nearly ferromagnetic superconductors have recently garnered intense interests due to their potential for topolofically protected excitations. On the flip side, it is hoped that a better understanding of proximate ferromagnetic phases can give insight into the superconducting regimes. Here we study the magnetotransport of a novel nearly superconducting ferromagnet across a quantum phase transition induced by pressure.   

Evolution of short-range magnetic fluctuations in disordered ferromagnetic alloys.

We present small-angle neutron scattering (SANS) results on NiV to trace the evolution of the short-range magnetic clusters in a ferromagnetic alloy. NiV is a simple ferromagnetic (FM) alloy with random atomic distribution that undergoes a quantum phase transition from an FM to a paramagnetic state with sufficient substitution of Ni by V. The onset of FM order below transition temperature (Tc) vanishes towards x_c=0.116, indicating a quantum critical point (QCP) with signatures of the disorder [1]. We collected full polarized SANS data on different polycrystalline NiV samples close to the QCP at NG7SANS, NCNR, NIST. Through the angular dependence (of the spin-flip (SF) and DIF signal, the non-SF flipper contrast) with the magnetic field transverse to the beam, we succeed in resolving the small magnetic scattering at diverse lengths scales within the FM state well below Tc<50K [2]. Besides isotropic magnetic short-range correlations that remain at very low temperatures, we find an anisotropic magnetic contribution that reveals large-scale magnetic domains below T_c.

We present how the clusters within the FM phase are affected by an external magnetic field. The SF data (at higher Q>0.1nm^-1) reveal gradual freezing of fluctuations, while the DIF data (at the lower Q<0.2nm^-1) show an increase in domain scattering with increasing field. Getting closer to x_c, the magnetic clusters become more dominant than the ordered phase, but the small magnetic signals are more challenging to resolve for more specific details. However, the data agree with qualitative expectations of a disordered QCP. They reveal magnetic clusters in NiV with signatures of a range of dynamics that mark a quantum Griffith's phase.

[1] R. Wang et al, Phys. Rev. Lett. 18, 267202 (2017)

[2] A. Schroeder et al, AIP Adv.10,015036 (2020)   

Quantum critical point and phase separation at finite doping in Hund metals.

"Hund metals”  are multi-orbital paramagnetic metals with sizeable effects due to the intra-atomic exchange energy or Hund’s coupling, and are characterised by strong, orbital-selective correlations and large fluctuating local magnetic moments. Their physics is relevant for iron-based superconductors and other materials like transition metal oxides.

A general feature found in models and realistic simulations of these materials, and corroborated by experimental data, is a frontier crossing the doping-interaction strength plane, and originating from the Mott transition point of the half-filled system, across which the aforementioned defining features are strongly enhanced.

This frontier is a cross-over at large doping while approaching half-filling it becomes a first-order transition between two metals. It features a phase separation zone ending in a quantum critical point at finite doping.

I will show that all this phenomenology is due to the first-order nature of the Mott transition and can be back-tracked to a small energy scale splitting the atomic ground-state multiplet, in this case the Hund’s coupling. 

I will highlight the perfect parallel with a leading scenario for the physics of the cuprates, and thus possibly a universal one for materials showing high-Tc superconductivity.   

Emergence of new quantum-critical magnetic ground state in pyrochlore iridate Sm2Ir2O7

Pyrochlore iridates, comprised of two inter-penetrating magnetic lattices of corner-sharing tetrahedra, are a complex and varied group of compounds under investigation into their exotic magnetic and electronic properties across condensed-matter physics. These magnetic tetrahedral networks order in fascinating all-in-all-out or 2-in-2-out radial spin arrangements. The study of quantum criticality, and the tuning of metal-insulator transitions, are already fertile areas for uncovering new phases of matter and understanding of fundamental physics - criticality of such an exotic form of magnetism has richer potential still. We report magnetic, transport and magnetotransport measurements on single crystals of Sm₂Ir₂O₇, in particular using applied pressure to tune magnetic order in the system and mapping the full pressure-temperature phase diagram up to 87 kbar. The all-in-all-out long-range order of the Ir sub-lattice which governs the ambient-pressure behaviour is shown to be suppressed to a quantum critical point at a critical pressure of around 63 kbar. Rather than observing the metal-insulator transition in this compound give way to metallic behaviour as Ir order is removed, we report instead a secondary mechanism taking over the gapping of electrical transport, and the weak-insulator state persisting beyond the critical point. Within the Ir ordered phase at low pressures, we report a characteristic hysteresis in the magnetoresistance we equate to that previously seen in Ho₂Ir₂O₇, but with a far larger saturation field. Finally, in the vicinity of the quantum critical point we uncover the emergence of a new state described by a weaker hysteresis and a negative magnetoresistance. We suggest this to be due to the weak Sm-Sm interactions becoming dominant and driving a new form of order.   

Dynamics of the critical phonon modes in quantum paraelectric SrTiO3

Proximity of SrTiO₃ to a quantum critical point [1] and evolution of underlying modes when tuned with even with modest pressure has become a promising new branch of study of quantum critical phenomena. The critical point here is associated with a soft optical phonon mode responsible for the ferroelectricity instability through a continuous displacive transition. Our recent dielectric measurements under pressure [2] exposed formation of a ‘quantum optical-acoustic state’ around 2K. Further to this, we performed triple-axis inelastic neutron scattering experiments on single-crystal STO down to 37 mK to directly observe the optical and acoustic (and hybridised) modes at and around q=0 in the multiple directions of the reciprocal space. In addition, we explored how the pressure affects the phonon mode in STO up to 5.0 kbar around 2K. Our observations shed light on the coupling of the soft optical mode with the acoustic phonons, and its response to external pressure [3]. We believe this could help us understand the importance of anharmonic lattice dynamics and unusual thermal transport in STO.  

[1] S. E. Rowley, et al. Nat. Phys., 10(5), 367–372 (2014)

[2] M. J. Coak et al., PNAS, 117, 12707 (2020)

[3] M. J. Coak, et al. Phys. Rev. B, 100 214111 (2019)   

Emergent Rokhsar-Kivelson point in realistic quantum Ising models

We demonstrate that in triangular lattice quantum Ising antiferromagnets, the seemingly trivial first-order transition between the clock and stripe phases is associated with quantum critical behaviors. This phase transition is driven by proliferation of domain walls between clock domains, where the domain wall tension vanishes at the critical point. We present its relation to the Rokhsar-Kivelson deconfined quantum critical point in quantum dimer models. We discuss experimental signatures of this quantum critical point. We propose that such critical point may be realized in the rare-earth material TmMgGaO₄ by applying hydrostatic pressure. We also discuss potential experimental realization in programmable Rydberg arrays.