Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session L19: Precision Many Body Physics VIII |
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Sponsoring Units: DCOMP DAMOP DCMP Chair: Olga Goulko, Boise State University Room: BCEC 156C |
Wednesday, March 6, 2019 11:15AM - 11:51AM |
L19.00001: Entanglement production and information scrambling in a noisy spin system Michael Knap We study theoretically entanglement and operator growth in a spin system coupled to an environment, which is modeled with classical dephasing noise. Using exact numerical simulations we show that the entanglement growth and its fluctuations are described by the Kardar-Parisi-Zhang equation. Moreover, we find that the wavefront in the out-of-time ordered correlator (OTOC), which is a measure for the operator growth, propagates linearly with the butterfly velocity and broadens diffusively with a diffusion constant that is larger than the one of spin transport. The obtained entanglement velocity is smaller than the butterfly velocity for finite noise strength, yet both of them are strongly suppressed by the noise. We calculate perturbatively how the effective time scales depend on the noise strength, both for uncorrelated Markovian and for correlated non-Markovian noise. |
Wednesday, March 6, 2019 11:51AM - 12:03PM |
L19.00002: Real time correlations and spectral functions in numerical linked-cluster expansions Ehsan Khatami Highly precise static properties of strongly correlated fermions at finitie temperatures from numerical linked-cluster expansions have been widely used to characterize systems of ultracold atoms in optical lattices. Here, I will discuss how dynamical properties such as various spectral functions of quantum lattice models can be obtained using the method through real time, as opposed to imaginary time, correlation functions at temperatures relevant to current optical lattice experiments. Nichols et al., arXiv:1802.10018 |
Wednesday, March 6, 2019 12:03PM - 12:15PM |
L19.00003: Thermodynamics of the disordered Hubbard model from numerical linked-cluster expansions Jacob Park, Richard Theodore Scalettar, Ehsan Khatami The interplay of disorder and strong correlations in quantum many-body |
Wednesday, March 6, 2019 12:15PM - 12:27PM |
L19.00004: Low-energy physics of the bilinear-biquadratic spin-1 chain Moritz Binder, Thomas Barthel The bilinear-biquadratic spin-1 chain features various interesting quantum phases, including the Haldane phase, a dimerized phase, and an extended critical phase. Here, we apply an efficient density matrix renormalization group (DMRG) algorithm utilizing infinite boundary conditions to compute precise dynamic spin structure factors for a comprehensive set of points in the phase diagram. Analyzing both dynamic spin and quadrupolar correlations, we gain detailed insights into the nature of low-lying excitations of the model. We compare our results to Bethe ansatz solutions at the SU(3)-symmetric ULS point and the TB point as well as at the pure biquadratic point, which can be mapped to an anisotropic spin-1/2 XXZ chain in the gapped Néel phase. In the Haldane phase, we relate our results to the approximate description in terms of the non-linear sigma model. |
Wednesday, March 6, 2019 12:27PM - 12:39PM |
L19.00005: Ground states of a J-Q model with long-range antiferromagnetic interactions Sibin Yang, Dao-Xin Yao, Anders W Sandvik We employ large-scale sign-free quantum Monte Carlo and Lanczos exact diagonalization to study the 1D J-Q model (a Heisenberg antiferromagnetl with multi-spin couplings added) with long-range interactions. Three phases, an ordered anti-ferromagnet (AFM), a quasi long-range ordered (QLRO state), and a valence bond solid (VBS), are identified by applying Binder-cumulant and level-crossing methods. We investigate different characteristics of these phases and their quantum phase transitions. From our numerical data and for the model we studied, the Binder-cumulant method has advantages in determining the quantum critical AFM-QLRO point and a certain range of the QLRO-VBS transition line, while the level crossing method is more suitable for the other region of QLRO-VBS transition. In addition, there could be a direct quantum phase transition between the AFM and VBS phases, possibly an analog of the 2D deconfined quantum critical point (DQCP) in one dimension. |
Wednesday, March 6, 2019 12:39PM - 12:51PM |
L19.00006: Nature of spin-liquid phase in 2D spin-1/2 J_1-J_2 triangular antiferromagnet Tigran Sedrakyan, Roderich Moessner, Alex Kamenev We study the stability of ordered states in a two-dimensional quantum spin-1/2 J_1-J_2 XY antiferromagnet on a frustrated triangular lattice using composite fermion representation of spins. In the presence of next-nearest-neighbor antiferromagnetic coupling, J_2, the model is shown to undergo a continuous transition from $120^\circ$ ordered state to a quantum U(1) Dirac spin-liquid (QED_3) at J_2/J_1 ~ 0.089, in accordance with previous variational Monte-Carlo and DMRG studies. In the XY limit, the U(1) gauge field emerges in a narrow parameter interval of 0.089\lesssim J_2/J_1 \lesssim 0.116, that stabilizes the spin liquid. The transition to the tripe phase at J_2/J_1 \sim 0.116 is found to be of first order. Finite Ising interaction, J_z, pushes the boundaries of the phase transitions to $120^\circ$ state and the stripe ordered state apart, thus opening a wider interval for the spin-liquid. Our results show an interesting interplay of ordering and the emergence of the gauge field in the vicinity of unconventional criticality. |
Wednesday, March 6, 2019 12:51PM - 1:03PM |
L19.00007: Anomaly matching and symmetry-protected critical phases in SU(N) spin systems in 1+1 dimensions Yuan Yao, Chang-Tse Hsieh, Masaki Oshikawa We study (1+1)-dimensional SU(N) spin systems in the presence of the global SU(N) rotation and lattice translation symmetries. By matching the mixed anomaly of the PSU(N)×Z in the continuum limit, we identify a topological index for spin model evaluated as the total number of Young-tableaux boxes of spins per unit cell modulo N, which characterizes the "ingappability" of the system. A nontrivial index implies either a ground-state degeneracy in a gapped phase, which can be regarded as a field-theory version of the Lieb-Schultz-Mattis theorem, or a restriction of the possible universality classes in a critical phase (symmetry-protected critical phase) -- only a class of SU(N) Wess-Zumino-Witten theories can be realized in the low-energy limit of the given lattice model in the presence of the symmetries. Similar constraints also apply when a higher global symmetry emerges in the model with a lower symmetry. Our prediction agrees with several examples known in previous studies of SU(N) models. |
Wednesday, March 6, 2019 1:03PM - 1:15PM |
L19.00008: Efficient generation of many-body entangled states by multilevel oscillations Peng Xu We propose a fast method utilizing multilevel oscillations to generate high-fidelity massive entangled states in an antiferromagnetic spin-1 Bose-Einstein condensate (BEC). Combing the multilevel oscillations with additional adiabatic drives, we greatly shorten the necessary evolution time and relax the requirement on the control accuracy of quadratic Zeeman splitting, from micro-Gauss to milli-Gauss, for a 23Na spinor BEC. The achieved high fidelities over 96% show that two kinds of massively entangled states, the many-body singlet state and the twin-Fock state, are almost perfectly generated. The generalized spin squeezing parameter drops to a value far below the standard quantum limit even with the presence of particle number fluctuations and stray magnetic fields, illustrating the robustness of our protocol under real experimental conditions. The generated many-body entangled states can be employed to achieve the Heisenberg-limit quantum precision measurement and to attack nonclassical problems in quantum information science. |
Wednesday, March 6, 2019 1:15PM - 1:27PM |
L19.00009: Efficient Two Dimensional Tensor Network Algorithms for Systems with Long-Range Interactions Matthew O'Rourke, Zhendong Li, Garnet Chan Current state-of-the-art tensor network algorithms in two dimensions, the most predominant being infinite projected entangled-pair states (iPEPS), have not yet advanced beyond the study of local lattice models. In order to utilize the power of these methods to study systems with physically realistic long-range interactions, we discuss a practical and efficient representation of the Hamiltonian of such systems as a projected entangled-pair operator (PEPO). We express the long-range interaction as a linear combination of correlation functions of an auxiliary system with only nearest neighbor interactions. This construction yields a long-range PEPO as a sum of ancillary PEPOs, each of small, constant bond dimension. Applications of this PEPO formulation to iPEPS simulations of model systems will be discussed. |
Wednesday, March 6, 2019 1:27PM - 1:39PM |
L19.00010: Solving constrained counting problems with tensor networks Stefanos Kourtis In this talk, I will present newly developed physics-inspired methods for the solution of counting constraint satisfaction problems (#CSPs). #CSP instances can be reformulated as models of interacting degrees of freedom, whose zero-temperature partition function represents the volume of the solution manifold. I will introduce practical methods to compute such partition functions based on tensor network contraction. In this formulation, computational complexity can be viewed as a manifestation of quantum entanglement, and controlling the growth of entanglement throughout tensor network contraction can yield a significant computation speedup. Using some hard counting problems as benchmarks, I will demonstrate that tensor network methods can be a useful tool for solving some hard classes of #CSPs. I will conclude with an outline of ongoing work on extensions of this framework. |
Wednesday, March 6, 2019 1:39PM - 1:51PM |
L19.00011: Non-Abelian symmetries in thermal tensor network states Bin-Bin Chen, Wei Li, Andreas Weichselbaum The implementation of non-Abelian symmetries in the tensor networks greatly improves efficiency and thus also precision of quantum many-body simulations in quasi-1D systems. Here, in particular, we discuss our general implementation of the SU(2) spin together with U(1) charge symmetry based on the QSpace [1] tensor library in the recently developed thermal tensor network simulations including the series expansion thermal tensor network (SETTN) [2], and exponential thermal renormalization group (XTRG) [3]. We will also show benchmarks of the fermionic Hubbard model on both square and triangular lattice. |
Wednesday, March 6, 2019 1:51PM - 2:03PM |
L19.00012: Exponential Thermal Tensor Network Approach for Quantum Lattice Models Andreas Weichselbaum, Bin-Bin Chen, Lei Chen, Ziyu Chen, Wei Li We speed up thermal simulations of quantum many-body systems in one- (1D) and two-dimensional (2D) models in an exponential way by iteratively projecting the thermal density matrix ρ≡e^{-βH} onto itself. We refer to this approach as the exponential tensor renormalization group (XTRG) [1]. It is in stark contrast to conventional Trotter-Suzuki-type methods which employ a linear quasi-continuous grid in inverse temperature β≡1/T. By avoiding Trotterization alltogether, XTRG can also deal with longer-range interactions in a straightforward algorithmic way. By construction, XTRG can reach exponentially low temperatures by a linear number of iterations, and thus not only saves computational time but also merits better accuracy due to significantly fewer truncation steps. More fine-grained temperature resolution can be achieved via simple interleaving of data sets. We work in an (effective) 1D setting exploiting matrix product operators (MPOs) which allows us to fully and uniquely implement non-Abelian and Abelian symmetries to greatly enhance numerical performance. We show exemplary XTRG results for Heisenberg models on 1D chains and 2D lattices with a finite temperature phase transition down to low temperatures approaching ground state properties. [1] Phys. Rev. X 8, 031082 (2018) |
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