Quantum magnetism and criticality (original) (raw)
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Quantum criticality and black holes
Journal of Physics-condensed Matter, 2009
Many condensed matter experiments explore the finite temperature dynamics of systems near quantum critical points. Often, there are no well-defined quasiparticle excitations, and so quantum kinetic equations do not describe the transport properties completely. The theory shows that the transport co-efficients are not proportional to a mean free scattering time (as is the case in the Boltzmann theory of quasiparticles), but are completely determined by the absolute temperature and by equilibrium thermodynamic observables. Recently, explicit solutions of this quantum critical dynamics have become possible via the AdS/CFT duality discovered in string theory. This shows that the quantum critical theory provides a holographic description of the quantum theory of black holes in a negatively curved anti-de Sitter space, and relates its transport co-efficients to properties of the Hawking radiation from the black hole. We review how insights from this connection have led to new results for experimental systems: (i) the vicinity of the superfluid-insulator transition in the presence of an applied magnetic field, and its possible application to measurements of the Nernst effect in the cuprates, (ii) the magnetohydrodynamics of the plasma of Dirac electrons in graphene and the prediction of a hydrodynamic cyclotron resonance. this state, but there is a well-developed theory of the transport properties of the TL liquid. Historically, this theory evolved over several decades of research on quantum many body systems in one dimension. Key in the historical development were exact solutions of model Hamiltonians via the Bethe Ansatz. Insights gained from the structure of excitations in the Bethe Ansatz solutions led to a more general understanding of the low energy excitations of a generic Hamiltonian, and a universal low energy theory of the TL liquid. Thus while the exact solutions were restricted to artificial models, they played a key role in the development of the general theory. Of course, after the fact, with the general theory of the TL liquid before us, we can justify it in its own terms, and largely dispense with reference to the Bethe Ansatz solutions.
Quantum critical point in the superconducting transition on the surface of a topological insulator
Physical Review B, 2014
Pairing in the Weyl semi -metal appearing on the surface of topological insulator is considered. It is shown that due to an "ultra-relativistic" dispersion relation there is a quantum critical point governing the zero temperature transition to a superconducting state. Starting from the microscopic Hamiltonian with local attraction, we calculated using the Gor'kov equations, the phase diagram of the superconducting transition at arbitrary chemical potential, its magnetic properties and critical exponents close to the quantum critical point. The Ginzburg -Landau effective theory is derived for small chemical potential allowing to consider effects of spatial dependence of order parameters in magnetic field. The GL equations are very different from the conventional ones reflecting the chiral universality class of the quantum phase transition. The order parameter distribution of a single vortex is found to be different as well. The magnetization near the upper critical field is found to be quadratic, not linear as usual. We discuss the application of these results to recent experiments in which surface superconductivity was found that some 3D topological insulators and estimate feasibility of the phonon pairing.
Journal of High Energy Physics
We consider the magneto-transports of quantum matters doped with magnetic impurities near the quantum critical points(QCP). For this, we first find new black hole solution with hyper-scaling violation which is dual to such system. By considering the fluctuation near this exact solution, we calculated all transport coefficients using the holographic method. We applied our result to the surface state of the topological insulator with magnetic doping and found two QCP's, one bosonic and the other fermionic. It turns out that doped Bi 2 Se 3 and Bi 2 Te 3 correspond to different QCP's. We also investigated transports of QCP's as functions of physical parameters and found that there are phase transitions as well as crossovers from weak localization to weak anti-localization.
2020
We consider the magneto-transports of quantum matters doped with magnetic impurities near the quantum critical points(QCP). For this, we first find new black hole solution with hyper-scaling violation which is dual to such system. By considering the fluctuation near this exact solution, we calculated all transport coefficients using the holographic method. We applied our result to the surface state of the topological insulator with magnetic doping and found two QCP's, one bosonic and the other fermionic. It turns out that doped Bi_2Se_3 and Bi_2Te_3 correspond to different QCP's. We also investigated transports of QCP's as functions of physical parameters and found that there are phase transitions as well as crossovers from weak localization to weak anti-localization.
Link between magnetic field-induced quantum criticality and phase formation in
Physica B: Condensed Matter, 2005
The magnetization and resistivity studies in magnetic fields up to 45 T were used to establish magnetic field versus temperature phase diagram and quantum criticality in UðRu 1Àx Rh x Þ 2 Si 2 : For x ¼ 4%; the hidden order is completely destroyed, stabilizing a single field-induced phase II. A correlation between the field dependence of this phase and that of the quantum critical point, combined with the suppression of the T 2 coefficient of the resistivity within it, shows that the field-tuned quantum criticality is intimately related to the phase formation. r
Quantum criticality: beyond the Landau-Ginzburg-Wilson paradigm
Physical Review B, 2004
We present the critical theory of a number of zero temperature phase transitions of quantum antiferromagnets and interacting boson systems in two dimensions. The most important example is the transition of the S = 1/2 square lattice antiferromagnet between the Néel state (which breaks spin rotation invariance) and the paramagnetic valence bond solid (which preserves spin rotation invariance but breaks lattice symmetries). We show that these two states are separated by a secondorder quantum phase transition. This conflicts with Landau-Ginzburg-Wilson theory, which predicts that such states with distinct broken symmetries are generically separated either by a first-order transition, or by a phase with co-existing orders. The critical theory of the second-order transition is not expressed in terms of the order parameters characterizing either state, but involves fractionalized degrees of freedom and an emergent, topological, global conservation law. A closely related theory describes the superfluid-insulator transition of bosons at half-filling on a square lattice, in which the insulator has a bond density wave order. Similar considerations are shown to apply to transitions of antiferromagnets between the valence bond solid and the Z2 spin liquid: the critical theory has deconfined excitations interacting with an emergent U(1) gauge force. We comment on the broader implications of our results for the study of quantum criticality in correlated electron systems.
Nature communications, 2017
The superconductor-insulator transition (SIT) is considered an excellent example of a quantum phase transition that is driven by quantum fluctuations at zero temperature. The quantum critical point is characterized by a diverging correlation length and a vanishing energy scale. Low-energy fluctuations near quantum criticality may be experimentally detected by specific heat, cp, measurements. Here we use a unique highly sensitive experiment to measure cp of two-dimensional granular Pb films through the SIT. The specific heat shows the usual jump at the mean field superconducting transition temperature marking the onset of Cooper pairs formation. As the film thickness is tuned towards the SIT, is relatively unchanged, while the magnitude of the jump and low-temperature specific heat increase significantly. This behaviour is taken as the thermodynamic fingerprint of quantum criticality in the vicinity of a quantum phase transition.
Quantum-critical phase from frustrated magnetism in a strongly correlated metal
Nature Physics, 2019
Strange-metal phenomena often develop at the border of antiferromagnetic order in strongly correlated metals. It has been well established that they can originate from the fluctuations anchored by the point of continuous quantum phase transition out of the antiferromagnetic order, i.e., a quantum critical point. What has been unclear is how these phenomena can be associated with a potential new phase of matter at zero temperature. Here we show that magnetic frustration of the 4f-local moments in the distorted Kagome intermetallic compound CePdAl gives rise to such a paramagnetic quantum-critical phase. Moreover, we demonstrate that this phase turns into a Fermi liquid through a Mott-like crossover; in a two-dimensional parameter space of pressure and magnetic field, this crossover is linked to a line of zero-temperature 4f-electron localization-delocalization phase transitions at low and moderate pressures. Our discovery motivates a new design principle for strongly correlated metallic states with unconventional excitations that may underlie the development of such effects as high temperature superconductivity. Geometrical frustration in quantum-spin systems gives rise to quantum fluctuations which may suppress long-range magnetic order and cause a quantum-spin-liquid ground state [1]. This notion is traditionally associated with insulating magnets only. There has been increasing recognition, however, that geometrical frustration is also important to bad metals that host local moments, such as strongly correlated f-electron metals [2-7], which provide a prototype setting
Finite-size criticality in fully connected spin models on superconducting quantum hardware
2022
The emergence of a collective behavior in a many-body system is responsible of the quantum criticality separating different phases of matter. Interacting spin systems in a magnetic field offer a tantalizing opportunity to test different approaches to study quantum phase transitions. In this work, we exploit the new resources offered by quantum algorithms to detect the quantum critical behaviour of fully connected spin−1/2 models. We define a suitable Hamiltonian depending on an internal anisotropy parameter γ, that allows us to examine three paradigmatic examples of spin models, whose lattice is a fully connected graph. We propose a method based on variational algorithms run on superconducting transmon qubits to detect the critical behavior for systems of finite size. We evaluate the energy gap between the first excited state and the ground state, the magnetization along the easy-axis of the system, and the spin-spin correlations. We finally report a discussion about the feasibility of scaling such approach on a real quantum device for a system having a dimension such that classical simulations start requiring significant resources.