Bulletin of the American Physical Society
APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017; New Orleans, Louisiana
Session A20: Quantum Phase Transitions I |
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Sponsoring Units: DCMP Chair: Liusuo Wu Room: 280 |
Monday, March 13, 2017 8:00AM - 8:12AM |
A20.00001: Quantum Critical Point revisited by the Dynamical Mean Field Theory Wenhu Xu, Gabriel Kotliar, Alexei Tsvelik Dynamical mean field theory is used to study the quantum critical point (QCP) in the doped Hubbard model on a square lattice. The QCP is characterized by a universal scaling form of the self energy and a spin density wave instability at an incommensurate wave vector. The scaling form unifies the low energy kink and the high energy waterfall feature in the spectral function, while the spin dynamics includes both the critical incommensurate and high energy antiferromagnetic paramagnons. We use the frequency dependent four-point correlation function of spin operators to calculate the momentum dependent correction to the electron self energy. Our results reveal a substantial difference with the calculations based on the Spin-Fermion model which indicates that the frequency dependence of the the quasiparitcle-paramagnon vertices is an important factor. [Preview Abstract] |
Monday, March 13, 2017 8:12AM - 8:24AM |
A20.00002: Line of Critical points protected by dynamical constraint Z. Dai, Adam Nahum We studied the scaling structure of the 2+1D critical quantum loop gas models first proposed by Michael Freedman et al. These models describe a line of quantum critical points with no known field theory description but with connections to topological phase transitions. We found them to be a generic line of critical points under the no-reconnection constraint. This dynamical constraint is preserved under RG and leads to a new universality class. Through a correspondence between the ground state of the quantum model and the 2D classical loop gas, we are able to calculate the equal-time correlation function and identify the scaling dimension for every local operator. This correspondence further extends to the dynamics of both sides, thus allow the determination of the dynamical exponent through simulations on a classical relaxation process. Numerical results on honeycomb lattice with 500*500 plaquettes yielded a dynamical exponent of 3 along the line. [Preview Abstract] |
Monday, March 13, 2017 8:24AM - 8:36AM |
A20.00003: A critical fixed point of QED$_3$ with quenched disorder Alex Thomson, Subir Sachdev Quantum electrodynamics in 2+1-dimensions (QED$_3$) describes a critical phase of matter known as the algebraic spin liquid. It is a strongly coupled conformal field theory with a U(1) gauge boson coupled to 4$N_f$ two-component massless fermions. At $N_f=1$, this is a proposed ground state of the spin-1/2 kagome Heisenberg antiferromagnet. We study the behaviour of QED$_3$ in the presence of weak quenched disorder in its two spatial directions. When the disorder explicitly breaks the fermion flavour symmetry from SU($4N_f$)$\rightarrow$U(1)$\times$SU($2N_f$), we find that the theory flows to a non-trivial critical point with a dynamical critical exponent $z>1$. At this critical point, we determine the zero-temperature spin conductivity. Our calculations are done in the large-$N_f$ limit and the disorder is handled using the replica method. [Preview Abstract] |
Monday, March 13, 2017 8:36AM - 8:48AM |
A20.00004: Revealing quantum Griffiths singularities inside the ferromagnetic phase Adane Gebretsadik, Ruizhe Wang, Sara Ubaid-Kassis, Almut Schroeder, Thomas Vojta, P. J. Baker, F. L. Pratt, S. J. Blundell, T. Lancaster, I. Franke, J. S. M\"oller We present low-temperature inhomogeneous magnetic properties of the d-metal alloy Ni$_{1-x}$V$_x$ close to the quantum critical concentration $x_c \approx 11.6\%$ where the ferromagnetic transition temperature is suppressed to zero. The magnetization $M$ displays a singular dependence on the magnetic field $H$ not just in the paramagnetic phase ($x>x_c$) but also in the ferromagnetic phase ($x< x_c$). It is well described by a nonuniversal power law, $M -M_0 \sim H^\alpha$ with $M_0$ being the spontaneous magnetization. The exponent $\alpha$ is strongly $x$-dependent, approximately symmetric in $x-x_c$, and decreases to zero at $x_c$. Muon spin rotation experiments in longitudinal magnetic fields and zero fields in the ferromagnetic phase demonstrate inhomogeneous magnetic order and indicate the presence of dynamic fluctuating magnetic clusters. A similar cluster fraction can be estimated by both bulk of local probes that becomes significant close to $x_c$. These results provide strong evidence for a quantum Griffiths phase on the ferromagnetic side of the quantum phase transition. [Preview Abstract] |
Monday, March 13, 2017 8:48AM - 9:00AM |
A20.00005: Time-dependent real space RG on the spin-1/2 XXZ chain Peter Mason, Alexandre Zagoskin, Joseph Betouras In order to measure the spread of information in a system of interacting fermions with nearest-neighbour couplings and strong bond disorder, one could utilise a dynamical real space renormalisation group (RG) approach on the spin-1/2 XXZ chain. Under such a procedure, a many-body localised state is established as an infinite randomness fixed point and the entropy scales with time as log(log(t)). One interesting further question that results from such a study is the case when the Hamiltonian explicitly depends on time. Here we answer this question by considering a dynamical renormalisation group treatment on the strongly disordered random spin-1/2 XXZ chain where the couplings are time-dependent and chosen to reflect a (slow) evolution of the governing Hamiltonian. Under the condition that the renormalisation process occurs at fixed time, a set of coupled second order, nonlinear PDE's can be written down in terms of the random distributions of the bonds and fields. Solution of these flow equations at the relevant critical fixed points leads us to establish the dynamics of the flow as we sweep through the quantum critical point of the Hamiltonian. We will present these critical flows as well as discussing the issues of duality, entropy and many-body localisation. [Preview Abstract] |
Monday, March 13, 2017 9:00AM - 9:12AM |
A20.00006: Quantum Phase Transition of An Ising System Coupled to a Nuclear Spin Bath Ryan McKenzie The rare earth insulating magnet LiHoF$_4$ is often considered to be the quintessential (dipolar coupled) magnetic quantum Ising system. At low temperatures, upon application of a magnetic field transverse to the easy axis of the crystal, it undergoes a phase transition between ferromagnetic and paramagnetic states. However, neutron scattering experiments indicate this quantum phase transition is forestalled by the strong hyperfine coupling of each holmium ion's electronic spin to its nuclear spin. This spin bath environment appears to gap the crystal's excitation spectrum at its quantum critical point. This is relevant for the development of quantum computation, in which the coupling of a network of qubits to its environment must be mitigated or controlled in order to carry out meaningful computations. We show that the quantum phase transition in LiHoF$_4$ is preserved despite the presence of the nuclear spin bath, with spectral weight being transferred to a lower energy electronuclear mode that softens to zero at the quantum critical point. Hence, LiHoF$_4$ is indeed a paragon of a quantum Ising system in a transverse magnetic field. [Preview Abstract] |
Monday, March 13, 2017 9:12AM - 9:24AM |
A20.00007: Quantum phase transition of frustrated triangle lattice Ising model coupled to a fermi surface Zi Hong Liu, Xiao Yan Xu, Yang Qi, Zi Yang Meng Employing a newly developed quantum Monte Carlo algorithm, we investigate the frustrated transverse field triangle lattice Ising model coupled to a fermi surface. Without the coupling between Fermion and Ising fields, the bosonic system goes through a quantum phase transition from clock ordered phase to paramagnetic phase, where the quantum critical point (QCP) is associated with an emergent U(1) symmetry. With the coupling, the bosonic fluctuations introduced effective interaction among the fermions and have distorted the bare Fermi surface of the triangle lattice tight-binding model towards an interacting fermi surface with hot spots and fermi pockets. As the transverse field is gradually tuned towards to U(1) critical point, the gapped hot spots develop evidence of non-fermi-liquid behavoir, renders the original QCP in the frustrated triangle lattice Ising model even more non-trivial. The detailed properties of this QCP and its relevence towards recent developments of metallic QCP is also discussed. [Preview Abstract] |
Monday, March 13, 2017 9:24AM - 9:36AM |
A20.00008: Amplitude (Higgs) Mode at a Disordered Quantum Phase Transition Jack Crewse, Thomas Vojta, Daniel Arovas We investigate the amplitude (Higgs) mode of a diluted quantum rotor model in two dimensions close to the superfluid-Mott glass quantum phase transition. After mapping the Hamiltonian onto a classical (2$+$1)d XY model, scalar susceptibility is calculated in imaginary time by means of large-scale Monte Carlo simulations. Analytic continuation of the imaginary time data is performed via maximum entropy methods and yields the real-frequency spectral function. The spectral peak associated with the Higgs mode is identified and its fate upon approaching the disordered quantum phase transition is determined. [Preview Abstract] |
Monday, March 13, 2017 9:36AM - 9:48AM |
A20.00009: Quantum critical behavior of the superfluid-Mott glass transition Thomas Vojta, Jack Crewse, Martin Puschmann We investigate the zero-temperature superfluid to insulator transition in a diluted rotor model with particle-hole symmetry. We map the Hamiltonian onto a classical XY model with columnar disorder which we analyze by means of large-scale Monte Carlo simulations. For dilutions below the lattice percolation threshold, the system undergoes a generic superfluid-Mott glass transition. In contrast to other quantum phase transitions in disordered systems, its critical behavior is of conventional power-law type with universal (dilution-independent) critical exponents which we compute with high accuracy. In addition, we study the percolation quantum phase transition across the lattice percolation threshold; its critical behavior is governed by the lattice percolation exponents. We relate our results to a general classification of phase transitions in disordered systems, and we discuss experiments. [Preview Abstract] |
Monday, March 13, 2017 9:48AM - 10:00AM |
A20.00010: An explanation for the pseudogap states and the quantum phase transitions beneath the Dome Alejandro Genaro Cabo, Yoandri Vielza, Mauricio Domingues The work present the results of a model proposed to improve the understanding of the normal state of cuprate superconductors. The analysis reproduces the antiferromagnetic correlations and insulator character of these materials. Further, the discussion led to an outstanding prediction: the existence of well defined pseudogap states, which physical origin constitutes still today a debated question. The pseudogap emerges as a paramagnetic excited state, breaking the square crystal symmetry of the CuO planes in the same way as the AF order does it in the real material. The results defined the pseudogap effect as being of pure Coulomb origin. The Fermi surface exhibits the property defining its name: a momentum dependent gap which, that closes at the four corners of the Brillouin cell. The effect of the hole doping on both the AF-Insulator and the pseudogap states was investigated. The evolutions of the energy and band structure with hole doping, became able to predict the quantum phase transition (QPT) which La2CuO4 and other cuprate materials show at doping value, laying ``beneath'' the superconductor ``Dome''. The energies of the insulator and pseudogap states, both tend to coincide at a critical doping value of 0.2, at which the QPT is observed in the material. The doping evolution of the Fermi surface evaluated in for the insulator state, reproduce the experimental results for La2CuO4. [Preview Abstract] |
Monday, March 13, 2017 10:00AM - 10:12AM |
A20.00011: Rounding the First-Order Quantum Phase Transitions by Disorder in the Quantum Ashkin-Teller Model Ahmed K. Ibrahim, Thomas Vojta We study the influence of quenched disorder on the quantum phase transitions in the two-dimensional three-color quantum Ashkin-Teller model by Monte Carlo simulations. We show that in the weak-coupling regime the quenched disorder rounds the first-order quantum phase transition to a second-order one. This agrees with the predictions of a strong-disorder renormalization group analysis. However, in the strong-coupling regime there are two distinct transitions separating the paramagnetic, product and Baxter (ferromagnetic) phases. [Preview Abstract] |
Monday, March 13, 2017 10:12AM - 10:24AM |
A20.00012: 3D quantum liquid crystals by condensation of dislocation worldsheets Aron Beekman, Kai Wu, Jaakko Nissinen, Jan Zaanen A solid can partially melt into a liquid crystal where rotational rigidity is maintained while translational symmetry is restored. The topological melting is caused by an unbinding of dislocations. We recently provided a comprehensive review of quantum dislocation-mediated melting in 2D (arXiv:1603.04254). Through a duality mapping, phonons turn into dual gauge fields mediating interactions between dislocations. Upon condensation of dislocations, the dual gauge fields undergo the Anderson--Higgs mechanism and become gapped, signaling the loss of shear rigidity. Here we extend this theory to three dimensions. Dislocations are now linelike objects, strings, tracing out worldsheets in spacetime, while the dual gauge-fields become two-form (Kalb--Ramond) fields. We obtain the Higgs phase of these two-form gauge fields. Translational symmetry can be restored in three, two or one directions leading to nematic, smectic or columnar quantum liquid crystals. We derive the spectrum of low-energy excitations and its linear response. Goldstone modes due to broken rotational symmetry as well as superconductivity emerge whenever translational symmetry is restored. The peculiar features of liquid-crystalline order can be probed by finite-momentum spectroscopy. [Preview Abstract] |
Monday, March 13, 2017 10:24AM - 10:36AM |
A20.00013: Deconfined quantum critical points: symmetries and dualities Chong Wang, Adam Nahum, Max Metlitski, Cenke Xu, T. Senthil The deconfined quantum critical point (QCP) between the Neel and the valence bond solid (VBS) phases was proposed as an example of $(2+1)d$ conformal field theories that are fundamentally different from all the standard Landau-Ginzburg-Wilson-Fisher fixed points. In this work we demonstrate that the deconfined QCP, both the easy-plane version and the version with an explicit SU(2) spin symmetry, have multiple equivalent descriptions. In particular, the easy-plane deconfined QCP, besides its self-duality that was discussed before, is also dual to the $N_f = 2$ fermionic quantum electrodynamics (QED), which has its own self-duality and hence has an O(4)$\times Z_2^T$ symmetry; the deconfined QCP with the explicit SU(2) spin symmetry is dual to the $N_f = 2$ QED-Gross-Neveu fixed point, and could have an emergent SO(5) symmetry, as was conjectured before. [Preview Abstract] |
Monday, March 13, 2017 10:36AM - 10:48AM |
A20.00014: Entanglement entropy of the large $N$ Wilson-Fisher conformal field theory Seth Whitsitt, William Witczak-Krempa, Subir Sachdev We compute the entanglement entropy of the Wilson-Fisher conformal field theory (CFT) in 2+1 dimensions with O($N$) symmetry in the limit of large $N$ for general entanglement geometries. We show that the leading large $N$ result can be obtained from the entanglement entropy of $N$ Gaussian scalar fields with their mass determined by the geometry. For a few geometries, the universal part of the entanglement entropy of the Wilson-Fisher CFT equals that of a CFT of $N$ massless scalar fields. However, in most cases, these CFTs have a distinct universal entanglement entropy even at $N=\infty$. Notably, for a semi-infinite cylindrical region it scales as $N^0$ in the Wilson-Fisher theory, in stark contrast to the $N$-linear result of the Gaussian fixed point. [Preview Abstract] |
Monday, March 13, 2017 10:48AM - 11:00AM |
A20.00015: Indicators of Conformal Field Theory: entanglement entropy and multiple point correlators Pranay Patil, Ying Tang, Emanuel Katz, Anders Sandvik Entaglement entropy (EE) behavior is used as an indicator for conformal field theory (CFT) in many cases. Here we 2nd that it is not a reliable way to assess the existence of a conformal description as EE may show the same behavior even in the absence of a CFT. We use constraints on correlation functions given by the CFT to show that even though the EE shows the right behavior, the CFT is missing in the case of the Amplitude Product State in 1D at criticality. We also explore the CFT on the critical JQ2 chain in more detail using the behavior of two point and three point correlation functions. [Preview Abstract] |
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