Session P38: Quantum Criticality II

Quantum criticality in an itinerant antiferromagnet

Recent x-ray diffraction measurements have revealed a pressure-tuned continuous quantum phase transition in antiferromagnetic Cr [1]. High pressure transport results expose a crossover to a narrow fluctuation-dominated quantum critical regime at high pressure and low temperature. The discovery and description of a continuous quantum critical regime in this pure model system has broad implications for studies of quantum criticality and marginally magnetic materials. \\[4pt] [1] R. Jaramillo, Yejun Feng \textit{et al}. Nature \textbf{459}, 405 (2009).   

The Hall coefficient of quantum-critical Cr

Chromium is an itinerant antiferromagnet that exhibits a pressure-tuned continuous quantum phase transition [1]. The Hall coefficient is particularly sensitive to critical behavior in itinerant systems and magnetotransport measurements of single crystal Cr in a diamond anvil cell at low temperature reveal deviations from weak-coupling for P $\sim$ 10 GPa, We find a pseudogap-like regime of carrier deficiency for pressures just above the critical point. This behavior stands at odds with the behavior at the doping-driven quantum phase transition and helps elucidate the effects of quantum fluctuations without disorder. \\[4pt] [1] R. Jaramillo et al., Nature 459, 405 (2009).   

Nonequilibrium quantum criticality in bilayer itinerant ferromagnets

We present a theory of nonequilibrium quantum criticality in a bilayer system of itinerant electron magnets. The model consists of a first layer subjected to an inplane current and open to an external substrate. The second layer is closed and subject to no direct external drive, but couples to the first layer via spin exchange interaction. No particle exchange is assumed between the layers. We derive an effective action in terms of two coupled bosonic fields which are related to the magnetization fluctuations of the layers. In the absence of interlayer coupling, the bosonic modes possess different dynamical critical exponents z with z = 2 (z = 3) for the first (second) layer. This results in multiscale quantum criticality in the coupled system. It is shown that the low energy fixed point characterized by the larger dynamical exponent. The perturbative RG is used to study the correlation length in the quantum disordered and quantum critical regimes. We also derive the stochastic dynamics obeyed by the critical fluctuations in the latter regime.   

Quantum Fluctuations and Critical Behavior in NiCl$_{2}$-4SC(NH$_{2})_{2}$

NiCl$_{2}$-4SC(NH$_{2})_{2}$ is a anisotropic S = 1 system of Ni$^{2+}$ spins on a tetragonal lattice, that shows XY-type magnetic field-induced magnetic order below 1K. Here we report specific heat Cp(H) and magnetization M(H) vs field measurements on single crystal samples of this compound across the (H,T) phase boundaries. The specific heat shows a remarkable asymmetry for critical fields H$_{c1}$ and H$_{c2}$, against the expected particle-hole symmetry implicit in a hard-core boson approximation, pointing to strong quantum fluctuations effect. Our analysis of critical behavior in the magnetization at the (Hc1, Mc) phase boundary leads to the conclusion that the $U(1)$ symmetry is preserved, a characteristic of the Bose-Einstein condensation universality. Our Quantum Monte Carlo simulations reproduce the experimental data exceedingly well.   

A novel ferromagnetic Kondo system MnBi-Pt

MnBi is one of few ferromagnetic materials possessing strong magneto-optical properties. In order to understand and control the structural, magnetic and electrical transport properties of MnBi based alloys, we have prepared Pt-alloyed MnBi thin films by sequential evaporation of Bi, Mn and Pt onto a glass substrate using an AJA e-beam evaporation system. The films have post annealed stoichiometry of Mn$_{55-x}$Pt$_{x}$Bi$_{45}$ (x = 0, 1.5, 3, 4.5). X-ray diffraction shows that Mn$_{55-x}$Pt$_{x}$Bi$_{45}$ thin films adopt a hexagonal NiAs-type structure with preferred c-axis orientation. All the films are strongly ferromagnetic at room temperature, although saturation magnetization decreases and coercivity increases with the substitution of Pt. We have observed that the electrical transport properties of MnBi are highly sensitive to external nonmagnetic impurities including Pt and show a Kondo effect at low temperatures. The origin of Kondo effect in the ferromagnetic MnBi lattice due to the substitution of a nonmagnetic impurity will be discussed.   

HfFe$_{1-x}$Ru$_x$Ga$_2$, Candidate for Ferromagnetic Quantum Criticality

We present a study of the magnetic and thermodynamic properties of HfFe$_{1-x}$Ru$_x$Ga$_2$ single crystals grown using flux techniques. Having found a low temperature ferromagnetic intermetallic compound HfFeGa$_2$ we try to suppress the Curie Temperature (T$_c$) by doping with Ru as a means to investigate the evolution of critical phenomena and perhaps realize a ferromagnetic quantum critical point (QCP). Magnetization measurements have shown changes in T$_c$ of HfFe$_{1-x} $Ru$_x$Ga$_2$ from approximately $48$K to below $1.8$K as a function of Ru concentration (x). We will show recent data as well as discuss the development of the spontaneous moment (m$_0 $), susceptibility \textbf{$\chi$} along with heat capacity upon doping and present the resulting magnetic phase diagram.   

Quantum Criticality in Coupled Spin-Dimer Systems

We examine the properties of coupled quantum spin-dimers in two dimensions within the quantum critical regime. We find that depending on the dimer arrangement, further terms appear in addition to the quantum non-linear sigma model in the low- energy effective action. While not present for a columnar dimer pattern and other previously studies dimerizations, they arise for a staggered arrangement of dimers. We propose further models, the dimerized honeycomb lattice and the herringbone lattice, where similar such terms appear. Our large-scale quantum Monte Carlo simulations show that the presence of such terms consistently leads to deviations from the expected universal scaling in the quantum critical regime. In addition, we contrast the spectral properties of these systems, and their response to non-magnetic impurities.   

Quantum phase transitions in kagome lattice quantum Heisenberg antiferromagnets with Dzyaloshinskii-Moriya interactions

Extending Sachdev's work (PRB 45 12377 (1992)) on kagome lattice quantum Heisenberg antiferromagnets, the system is studied including Dzyaloshinski-Moriya interaction (DMI) using Schwinger boson methods with Sp(N) symmetry. Above critical size of spin(S), we argue that two distinct types of ordered ground states are found. For small values of spin, the ordering disappears and we observe a quantum disordered ground state. The DMI favors ordering and when this is increased the system undergoes a quantum phase transition to an ordered state. We discuss the phase diagram of the system as a function of DMI strength and S/N.   

Topological Quantum Phase Transition in One-dimensional Spin Chain

We construct a Hamiltonian between AKLT and SZH model for one-dimensional S = 2 spin chain, where a variable parameter $\alpha$ is introduced. The edge spin is boson-like for AKLT model ($\alpha=0$), while fermion-like for SZH model($\alpha = 1$). Due to this distinction, topological quantum phase transition is predicted, and is addressed by large-scale DMRG calculation.   

The spin density wave transition and the genus expansion

A multitude of recent experiments on cuprates suggest that the underlying metallic state has a quantum critical point near optimal doping, which is masked by the superconducting dome. A natural possibility is that this critical point is associated with the onset of spin density wave order. In this talk, I will discuss the scaling theory of the spin density wave transition in two spatial dimensions. Previously, it has been suggested that the critical properties of the theory can be extracted using an expansion in the inverse number of fermion flavours N. I will discuss the RG flow of the theory to one loop and show that the 1/N expansion fails at low energies due to dynamical nesting of the fermi surface. Moreover, I will demonstrate that the naive large N counting fails at higher loop orders and has to be replace by the so-called ``genus'' expansion, whereby each diagram is classified by its topology. In particular, even when N is infinite one must still sum an infinite set of planar diagrams.   

Finite temperature quantum critical transport near the Mott transition

We use Dynamical Mean-Field Theory to study incoherent transport above the critical end-point temperature T$_{c}$ of the single band Hubbard model at half-filling. By employing an eigenvalue analysis for the free energy functional, we are able to precisely identify the crossover temperature T*(U) separating the Fermi liquid and the Mott insulating regimes. Our calculations demonstrate that a broad parameter range exist around the crossover line, where the family of resistivity curves displays simple scaling behavior. This is interpreted as a manifestation of quantum criticality controlled by the T=0 Mott transition, which is ``interrupted'' by the emergence of the coexistence dome at T $<$ T$_{c}$ . We argue that in situations where the critical temperature T$_{c}$ is significantly reduced, so that the coexistence region is reduced or even absent (as in two-band, particle-hole asymmetric models, where this is found even in the clean $d\to \infty $ limit [1, 2]), similar critical scaling properties should persist down to much lower temperatures, resembling quantum critical transport similar to that found in a number of experiments [2]. [1] A. Amaricci, G. Sordi, and M. J. Rosenberg, Phys. Rev. Lett. \textbf{101}, 146403 (2008) [2] A. Camjayi, K. Haule, V. Dobrosavljevic, and G. Kotliar, Nature Physics,\textbf{ 4}, 932 (2008)   

Topological Properties of Two-Dimensional Resonating-Valence-Bond States

We study the short-range resonating-valence-bond state on the two-dimensional square lattice, using Monte Carlo simulations with both loop-cluster and two-bond updates, combined with spin configurations sampled according to the singlet coverings. We calculate the four-spin (dimer-dimer) correlations and find that they decay as $r^{-\alpha}$ with $\alpha \approx 1.2$, instead of $\alpha=2$ as found in classical dimer model (which represents the ground state of the quantum dimer model at the Rokhsar-Kivelson critical point). Moreover, in different topological (winding number) sectors, these four-spin correlations, though having the same exponent $\alpha$, are affected by the presence of domain-wall like extended topological defects. By virtue of these defects, the different topological sectors should not be degenerate. We show that the bond energies grow with increasing winding number (which also corresponds to the number of domain walls).   

Determination of quantum critical point for superfluid-insulator transition in the disordered two-dimensional Bose-Hubbard model

We study superfluid-insulator transition for the disordered two- dimensional Bose-Hubbard model with quantum Monte Carlo simulations. Critical point for on-site Hubbard interaction strength $U_c$ is determined by finite-size scaling for fixed particle density $\rho=0.5$ and on-site disorder potential amplitude $\Delta=12$. We show that an extremely large number of disorder samples is required for such a calculation, implying that previous calculations based on a small number of disorder samples may not be reliable. At the critical point, we also compute the universal DC conductivity value to be $\sigma_ {\rm DC}=0.85\sigma_Q$, where $\sigma_Q=4e^2/h$ is conductivity ``quantum".   

Quantum Criticality Due to Incipient Phase Separation in the Two-dimentional Hubbard Model

We investigate the two-dimensional Hubbard model with next-nearest-neighbor hopping, $t^\prime$, using the dynamical cluster approximation. We confirm the existence of a first order phase separation transition terminating at a second order critical point at filling $n_c(t^\prime)$ and temperature $T_{ps}(t^\prime)$. We find that as $t\prime$ approaches zero, $T_{ps}(t^\prime)$ vanishes and $n_c(t^\prime)$ approaches the filling associated with the quantum critical point separating the Fermi liquid from the pseudogap phase. We propose that the quantum critical point under the superconducting dome is the zero temperature limit of the line of second order critical points.   

Thermodynamics of the quantum critical point at finite doping in the two-dimensional Hubbard model studied via the dynamical cluster approximation

We study the thermodynamics of the two-dimensional Hubbard model within the dynamical cluster approximation. We use continuous time quantum Monte Carlo as a cluster solver to avoid the systematic error which complicates the calculation of the entropy and potential energy (double occupancy). We find that at a critical filling, there is a pronounced peak in the entropy divided by temperature, $S/T$, and in the normalized double occupancy as a function of doping. At this filling, we find that specific heat divided by temperature, $C/T$, increases strongly with decreasing temperature and kinetic and potential energies vary like $T^2 \ln T$. These are all characteristics of quantum critical behavior.