Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session Z24: Quantum Many-Body Systems and Methods II |
Hide Abstracts |
Sponsoring Units: DCOMP Chair: Jia-An Yan, Towson University Room: 326 |
Friday, March 22, 2013 11:15AM - 11:27AM |
Z24.00001: Universal properties of the Higgs mode near quantum critical points Snir Gazit, Daniel Podolsky, Assa Auerbach Spontaneous symmetry breaking of relativistic models with $O(N)$ symmetry results in the emergence of two elementary excitations: the Goldstone modes and the Higgs mode. The massive Higss mode can decay into pairs of Goldstone modes, broadening the spectral line and hence questioning its visibility. Recently a set of \emph{scalar} response functions was introduced, in which the Higgs mode appears as a well defined peak [1]. We investigate the universal properties of the scalar susceptibility near the quantum critical point in 2+1 dimensions for $N=2$ and $N=3$ using Monte Carlo simulation. We demonstrate that the scalar spectral function contains a peak associated with the Higgs mode, which remains well-defined even upon approach to the critical point. We extract properties that characterize the Higgs peak, including the fidelity of the peak and the ratio $\omega_H/\Delta$ between the Higgs energy on the ordered side and the single particle gap on the disordered side. The universal nature of these results make them relevant to a broad range of experiments in condensed matter and atomic systems.\\[4pt] [1] D. Podolsky, A. Auerbach, and D. P. Arovas, Phys. Rev. B 84, 174522 (2011) [Preview Abstract] |
Friday, March 22, 2013 11:27AM - 11:39AM |
Z24.00002: Deconfined quantum criticality in bipartite SU($N$) antiferromagnets in two dimensions Matthew S. Block, Ribhu K. Kaul The theory of deconfined quantum criticality shatters the celebrated paradigm of the Landau-Ginzburg-Wilson description of phase transitions by allowing for direct, continuous, quantum phase transitions between conventional, ordered phases that spontaneously break fundamentally different symmetries of the system. In this talk, I will present new results of a quantum Monte Carlo study of a local, SU($N$) symmetric, antiferromagnetic spin model on the honeycomb and anisotropic rectangular lattices. In particular, I will show evidence for the existence of a continuous phase transition separating conventional N\'{e}el and valence bond solid ordered phases, as well as comparisons of the extracted critical exponents for sufficiently large values of $N$ to those calculated analytically via a $1/N$ expansion solution of the CP$^{N-1}$ gauge field theory that is believed to accurately describe the behavior at the critical point. In combination with previous results of a similar study on the square lattice, this allows for a robust understanding of how the existence of deconfined quantum criticality depends on the lattice symmetries as a function of $N$, and therefore gives a complete picture of the phenomenon in bipartite SU($N$) systems in two dimensions. [Preview Abstract] |
Friday, March 22, 2013 11:39AM - 11:51AM |
Z24.00003: Valence bond solid order and phase transitions of honeycomb lattice models Kenji Harada, Haruhiko Matsuo, Takafumi Suzuki, Synge Todo, Naoki Kawashima We investigate the ground states of generalized SU($N$) Heisenberg models on honeycomb lattices. From large-scale quantum Monte Carlo simulations, we confirm the columnar valence bond solid (c-VBS) orders for $N \ge 5$ at low temperatures, which corresponds to Kekul\'e distortion. It is consistent with Read and Sachdev's prediction[N.~Read and S.~Sachdev, Phys Rev B {\bf 42}, 4568 (1990)]. If we introduce the designed six-body interactions on hexagonal plaquettes, the c-VBS order occurs even in the SU(2) case. While the c-VBS state on a square lattice breaks $Z_4$ rotational symmetry, $Z_3$ rotational symmetry breaks on a honeycomb lattice. The difference may changes the nature of c-VBS phase. In particular, we will report phase transitions from a c-VBS phase to a paramagnetic or N\'eel phase in details. These results give us insight for deconfinement critical phenomena. [Preview Abstract] |
Friday, March 22, 2013 11:51AM - 12:03PM |
Z24.00004: Exotic quantum criticality in triangular lattice anti-ferromagnets Ribhu Kaul We introduce and study a generalized sign-problem free quantum anti-ferromagnet on the triangular lattice. Our Hamiltonian is shown to be a natural generalization of the popular bipartite SU($N$) anti-ferromagnet to non-bipartite lattices. At $N = 2$ our model is unitarily equivalent to a model of an XY superfluid (SF). Consistent with a large-N mapping to a certain quantum dimer model, we find evidence for valence bond solid (VBS) order with a large $\sqrt{12} \times\sqrt{12}$ unit cell. We show that there is a direct transition between these two phases that takes place between $N = 11$ and $N = 12$. For $N = 10, 11$ we use a four spin coupling parameter to tune through a new exotic ``deconfined'' continuous transition between SF and VBS. [Preview Abstract] |
Friday, March 22, 2013 12:03PM - 12:15PM |
Z24.00005: Efficient computation of GW energy level corrections for molecules described in a plane wave basis Bruno Rousseau, Jonathan Laflamme Janssen, Michel C\^ot\'e An efficient computational approach is presented to compute the ionisation energy and quasiparticle band gap at the level of the GW approximation when the Hilbert space is described in terms of plane waves. The method relies on ab initio calculations as a starting point. Then, the use of the Sternheimer equation eliminates slowly convergent sums on conduction states. Further, the Lanczos method is used to efficiently extract the most important eigenstates of the dielectric operator. This approach avoids the explicit computation of matrix elements of the dielectric operator in the plane wave basis, a crippling bottleneck of the brute force approach. The method is initially applied to organic molecules of current interest in the field of organic photovoltaics. Given the completeness of the plane wave basis, systematic convergence studies can be conducted. Furthermore, the method can readily be extended to describe polymers, which are also of interest for photovoltaic applications, but remain a significant computational challenge for methods based on localized basis sets. [Preview Abstract] |
Friday, March 22, 2013 12:15PM - 12:27PM |
Z24.00006: Thermodynamics of the 2D t-J Model William Putikka Very accurate calculations for the temperature dependence of the energy of the 2D Heisenberg AF on a square lattice have been done recently. By combining the results of these calculations with the known low temperature behavior of the Heisenberg entropy and results from high temperature series expansions at higher temperatures the Heisenberg entropy can be accurately calculated for all temperatures. This allows the Heisenberg entropy to be used as a known quantity in the calculation of the doped t-J model entropy. The high temperature series for the entropies of the t-J, Heisenberg and spinless fermion models can be combined as $S_{tJ}-S_{AF}(J^*)- S_{SF}(n^*)$ to produce a small difference which can then be extrapolated to low temperatures. Here $S_{AF}(J^*)$ is the Heisenberg entropy evaluated at a shifted value of $J$ and $S_{SF}(n^*)$ is the spinless fermion entropy evaluated at a modified density. By choosing $J^*$ and $n^*$ appropriately very good convergence for the series of the entropy differences can be obtained. The final t-J entropy is then found by readding the known functions $S_{AF}(J^*)$ and $S_{SF}(n^*)$. The integrated entropy is then fit to the high temperature free energy to find the ground state energy and the full temperature dependent free energy. [Preview Abstract] |
Friday, March 22, 2013 12:27PM - 12:39PM |
Z24.00007: ABSTRACT WITHDRAWN |
Friday, March 22, 2013 12:39PM - 12:51PM |
Z24.00008: Description of renormalization effect of multiband systems and its application within CMRA theory Jun Liu, Yongxin Yao, Chen Liu, Wencai Lu, Cai-Zhuang Wang, Kai-Ming Ho Many interesting physical phenomena, especially those observed in strongly correlated systems, incur a multiband description. A relatively accurate description of these systems is very important to clarify the origin of the observed physics. The recently proposed correlated matrix renormalization approximation (CMRA) introduces a new route to address this problem. As a variational approach, it makes use of possible renormalizations on the density matrix to correctly absorb effects resulting from strong electron-electron interactions. It performs quite well on different H systems. However, the generalization to multiband cases can be nontrivial. In this talk, I will discuss about how renormalization effects can be incorporated into the density matrix in the multiband case, and show the performance of the resulting CMRA on different dimer systems. [Preview Abstract] |
Friday, March 22, 2013 12:51PM - 1:03PM |
Z24.00009: Continuum limits of 12 flavor QCD Yannick Meurice |
Friday, March 22, 2013 1:03PM - 1:15PM |
Z24.00010: Condensation of Anyons in Frustrated Quantum Magnets Rolando Somma, Cristian Batista One dimensional quantum magnets can realize exotic states of matter such as Luttinger liquids, valence bond solids, and spin supersolids. A unique feature of 1D systems is that transmutations of particle statistics preserve the range and local nature of interactions. This is the main reason behind the success of spin-fermion transformations, such as the Jordan-Wigner mapping, for solving 1D quantum magnets. A simple generalization of such transformations allows for a mapping between spins and anyons, unusual particles that generalize the concepts of bosons and fermions. By exploiting this generalization, in this talk we will present the exact ground states of S$=$1/2 frustrated XXZ ladders, and introduce an efficient method for computing the relevant correlation functions. The novel states we find are \textit{anyon condensates} that spontaneously break the Hamiltonian symmetry associated with the particle-number conservation. In contrast to the familiar Bose-Einstein condensates, the condensed particles satisfy anyonic statistics. [Preview Abstract] |
Friday, March 22, 2013 1:15PM - 1:27PM |
Z24.00011: Fulde-Ferrell-Larkin-Ovchinnikov and topological superconducting phase in one dimensional optical lattice Ruilin Chu, An Zhao, Ming Gong, Shunqing Shen, Chuanwei Zhang The recent experimental realization of spin-orbit coupling in ultracold atom systems provides new arena for us to explore new quantum states. In this work, we explore the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase and topological superconducting phase of spin-orbital coupled Fermions in one dimensional optical lattice using the Density matrix renormalization group (DMRG) method. We demonstrate that the FFLO phase is energetically favored for in-plane Zeeman field while the topological superconducting phase is favored for out-of-plane Zeeman field. The entanglement entropy for these two phases are also examined. [Preview Abstract] |
Friday, March 22, 2013 1:27PM - 1:39PM |
Z24.00012: Probing Lee-Yang Zeros and Time-domain Phase Transitions Bo-Bo Wei, Ren-Bao Liu As a foundation of statistical physics, Lee and Yang in 1952 proved that the partition functions of thermal systems can be zero at certain points (called Lee-Yang zeros) on the complex plane of magnetic field. In the thermodynamic limit, the Lee-Yang zeros approach to real numbers at the critical temperature. However, the imaginary Lee-Yang zeros have not been regarded as experimentally observable since they occur at imaginary field or temperature, which are unphysical. Here we show that the coherence of a probe spin coupled to a many-body system presents zeros as a function of time that are one-to-one mapped to the Lee-Yang zeros of the many-body system. In the thermodynamic limit, of which the Lee-Yang zeros form a continuum, the probe spin coherence presents a sudden death and a sudden birth at critical times corresponding to the edge singularities of the Lee-Yang zeros. By measuring the probe spin coherence, one can directly reconstruct the partition function of a many-body system. These discoveries establish the concept of critical times for phase transition in analogue to critical temperature, and also provide a universal approach to studying interacting many-body systems through measuring coherence of only one probe spin (or one qubit in quantum computing). [Preview Abstract] |
Friday, March 22, 2013 1:39PM - 1:51PM |
Z24.00013: Strength of the effective Coulomb interaction at metal and insulator surfaces Ersoy Sasioglu, Christoph Friedrich, Stefan Bl\"{u}gel The effective on-site Coulomb interaction (Hubbard $U$) between localized electrons at surfaces of solids is expected to be enhanced due to the reduced coordination number and the subsequent reduced screening. By means of first-principles calculations in conjunction with the constrained random-phase approximation [1] within the FLAPW method, we show that this is indeed the case for simple metals and insulators but not necessarily for transition metals and insulators that exhibit pronounced surface states [2]. In the latter case, the screening contribution from surface states as well as the influence of the band narrowing can increase the electron polarization to such an extent that the expected decrease is overcompensated. In some cases the $U$ parameter is substantially reduced, e.g. by around 30\% for the Cr(100) surface, contrary to conventional wisdom. It also depends on the properties of the surface states for different surface orientations, e.g. 10\% [2\%] reduction [enhancement] of $U$ for MgO (110) [MgO (100)]. We show a systematic study for prototype materials including transition-metal surfaces.\\[4pt] [1] E. \c{S}a\c{s}{\i}o\u{g}lu et al., Phys. Rev. B 83, 121101(R) (2011). \newline [2] E. \c{S}a\c{s}{\i}o\u{g}lu et al., Phys. Rev. Lett. 109, 146401 (2012). [Preview Abstract] |
Friday, March 22, 2013 1:51PM - 2:03PM |
Z24.00014: A Symmetrized Basis for Transitions in the Heisenberg Model Roger Haydock, C.M.M. Nex The spin-S Heisenberg model has 2S+1 states on each site, for which there are (2S+1)$^{2}$ possible transitions between these states. For N sites there are (2S+1)$^{N}$ states and (2S+1)$^{2N}$ transitions between states. This rapid increase in the number of transitions with sites appears to limit calculations to just a few sites. However for transitions induced by spin-spin interactions, we construct a symmetrized basis which only grows as 2$^{N-3}$, making possible computations for much larger systems. [Preview Abstract] |
Friday, March 22, 2013 2:03PM - 2:15PM |
Z24.00015: Failure of the Holstein model to describe strong electron-phonon coupling Clemens P.J. Adolphs, Mona Berciu We point out an inconsistency in the most widely used theoretical models that describe systems with strong electron-phonon coupling. Both the Holstein and the Fr\"ohlich models assume that lattice distortions are sufficiently small to justify treating them to linear order. At strong coupling, however, it is well established that these models predict the formation of a small polaron, with potentially considerable local lattice distortions, invalidating the original assumption. Here we use the momentum average approximation to study the effect of higher-order coupling terms in the Holstein model. We show that they have drastic consequences on the properties of the polaron when compared to the linear model, and that these effects cannot be captured by a linear model with renormalized parameters. [Preview Abstract] |
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