Bulletin of the American Physical Society
APS March Meeting 2018
Volume 63, Number 1
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session S34: Precision Many Body Physics IVFocus
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Sponsoring Units: DCOMP DAMOP DCMP Chair: William Witczak-Krempa, University of Montreal Room: LACC 409A |
Thursday, March 8, 2018 11:15AM - 11:51AM |
S34.00001: Typical 1d quantum systems at finite temperatures can be simulated efficiently on classical computers Invited Speaker: Thomas Barthel It is by now well-known that ground states of gapped one-dimensional (1d) quantum-many body systems with short-range interactions can be studied efficiently using classical computers and matrix product state techniques. A corresponding result for finite temperatures was missing. |
Thursday, March 8, 2018 11:51AM - 12:03PM |
S34.00002: Continuous Matrix Product States for Quantum Field Theories with Broken Translational Invariance Martin Ganahl Continuous Matrix Product States (cMPS) are powerful variational ansatz states for continuous |
Thursday, March 8, 2018 12:03PM - 12:15PM |
S34.00003: Adiabatic Optimization of Tensor Networks Christopher Olund, Snir Gazit, John McGreevy, Norman Yao We present a novel algorithm for building a tensor network ground-state representation using adiabatic optimization. The basic idea follows the so-called s-source framework to construct a quantum circuit that interpolates between the ground state of system size L and 2L. This procedure can then be iterated to reach the thermodynamic limit. In contrast with standard algorithms which rely on the variational principle, our approach is based on the adiabatic theorem and may prove particularly useful for Hamiltonians where variational methods tend to fail. We propose an explicit numerical scheme for optimizing the interpolating quantum circuit and benchmark it against DMRG for several spin chain models; even near a quantum phase transition, where the spectral gap is small, we observe good agreement between the methods. |
Thursday, March 8, 2018 12:15PM - 12:27PM |
S34.00004: Gradient optimization of finite projected entangled pair states Lixin He, Wen-Yuan Liu, Shao-Jun Dong, Yong-Jian Han, G-C Guo The projected entangled pair states (PEPS) methods have been proved to be powerful tools to solve the strongly correlated quantum many-body problems in two-dimension. However, due to the high computational scaling with the virtual bond dimension D, PEPS are often limited to rather small bond dimensions. The optimization of the ground state using imaginary time evolution method with simple update scheme may go to a larger bond dimension. However, the accuracy of the rough approximation to the environment of the local tensors is questionable. We demonstrated that combining the Monte Carlo sampling techniques and gradient optimization will offer an efficient method to calculate the PEPS ground state. By taking the advantages of massive parallel computing, we can study the quantum systems with larger bond dimensions up to D=16 without resorting to any symmetry. Benchmark tests of the method on the J1-J2 model give impressive accuracy compared with exact results. |
Thursday, March 8, 2018 12:27PM - 12:39PM |
S34.00005: Extraction of Conformal Data in Critical Spin Chains Using the Koo-Saleur Formula and Periodic Uniform Matrix Product States Ashley Milsted, Yijian Zou, Guifre Vidal At a quantum critical point, the universal properties of a quantum spin chain are captured by an emergent conformal field theory (CFT). We propose and demonstrate new, generic techniques for characterizing the emergent CFT, given a local critical spin chain Hamiltonian, using the Koo-Saleur lattice representations of the Virasoro generators of conformal symmetry. In particular, we develop procedures for identifying the energy eigenstates of the spin chain corresponding to primary operators in the CFT, providing an essential part of the conformal data used to characterize the CFT. Furthermore, we show that periodic uniform Matrix Product States (puMPS), together with puMPS Bloch states, are excellent numerical means of extracting conformal data at large system sizes. Perhaps surprisingly, all low-energy excited states of the circular critical spin chain appear to be well captured by the Bloch-state ansatz. |
Thursday, March 8, 2018 12:39PM - 12:51PM |
S34.00006: Derivation of Matrix Product States for the Heisenberg Spin Chain with Open Boundary Conditions Zhongtao Mei, Carlos Bolech Using the algebraic Bethe Ansatz, we derive an exact matrix product representation of the Bethe-Ansatz states of the XXZ spin-1/2 Heisenberg chain with open boundary conditions. In this representation, the components of the Bethe eigenstates are expressed as traces of products of matrices that act on a tensor product of auxiliary spaces. As compared to the matrix product states of the same Heisenberg chain but with periodic boundary conditions, the dimension of the exact auxiliary matrices is enlarged as if the conserved number of spin-flips considered would have been doubled. Our method is generic for any non-nested integrable model, and we show this by deriving a matrix product representation of the Bethe eigenstates of the Lieb-Liniger model. Counterintuitively, the matrices do not depend on the spatial coordinate despite the open boundaries [1], and thus they suggest generic ways of exploiting translational invariance both for finite size and in the thermodynamic limit. // [1] Zhongtao Mei and C. J. Bolech, Phys. Rev. E 95, 032127 (2017). |
Thursday, March 8, 2018 12:51PM - 1:03PM |
S34.00007: Rényi Generalizations of the Operational Entanglement Entropy Hatem Barghathi, Adrian Del Maestro, Chris Herdman Entanglement in bipartite systems of indistinguishable particles could be reduced due to restrictions on the allowed local operations such as particle number conservation. In order to quantify such effects, Wiseman and Vaccaro [Phys. Rev. Lett. 91, 097902 (2003)] introduced an operational measure of the von Neumann entanglement entropy. Motivated by the difficulty of computing von Neumann entropies in quantum many-body systems, we introduce a Rényi generalization of the operational entanglement that is computationally and, potentially, experimentally accessible. Using the Widom conjecture, we investigate its scaling for free fermions in any dimension with the partition size and find that it has a logarithmically violated area law scaling, similar to the corresponding spatial entanglement, with at most, a double-log leading-order correction. By employing the correlation matrix method, we illustrate our theoretical findings in systems of up to 105 particles. |
Thursday, March 8, 2018 1:03PM - 1:15PM |
S34.00008: Operational entanglement of interacting spinless fermions in one-dimension Adrian Del Maestro, Hatem Barghathi, Emanuel Casiano-Diaz For indistinguishable itinerant particles subject to a super-selection rule fixing their total number, a portion of the spatial entanglement entropy in the ground state may be due solely to particle number fluctuations in the subregion and thus be inaccessible as a resource for quantum information processing. Excluding these contributions, we quantify the remaining operational entanglement in the t - V model of interacting spinless fermions in one spatial dimension via exact diagonalization. We find that it vanishes at the first order phase transition between a Tomonaga-Luttinger liquid and phase separated solid for attractive interactions and is maximal at the transition to the charge density wave for repulsive interactions. By examining the effects of filling fraction and partition size we explore the usefulness of the operational entanglement as a probe of quantum critical behavior. |
Thursday, March 8, 2018 1:15PM - 1:27PM |
S34.00009: Rigorous renormalization group at first-order phase transitions Johannes Motruk, Snir Gazit, Zeph Landau, Umesh Vazirani, Norman Yao The density matrix renormalization group (DMRG) has been a tremendously powerful method for computing the ground state of one-dimensional or quasi-one-dimensional quantum many-body systems. However, there can be situations that are particularly challenging for DMRG to solve owing to its local optimization procedure. One such example are first-order phase transitions where globally different states lie very close in energy so that DMRG may not converge to the true ground state, but to a local minimum in the energy landscape. Recently, a rigorous renormalization group (RRG) algorithm that employs a more global optimization approach, has been introduced. This algorithm targets a set of low-lying states instead of variationally searching for a single ground state. We compare the performance of both algorithms for typical spin chain models as well as near first-order phase transitions, where we observe improved reliability for RRG in certain cases. |
Thursday, March 8, 2018 1:27PM - 1:39PM |
S34.00010: Entanglement Branching Operator and its Applications Kenji Harada We introduce an entanglement branching operator to split a composite entanglement flow in a tensor network which is a promising theoretical tool for many-body systems. We can optimize an entanglement branching operator by solving a minimization problem based on squeezing operators. The entanglement branching is a new useful operation to manipulate a tensor network. For example, finding a particular entanglement structure by an entanglement branching operator, we can improve a higher-order tensor renormalization group method to catch a proper renormalization flow in a tensor network space. This new method yields a new type of tensor network states. The second example is a many-body decomposition of a tensor by using an entanglement branching operator. We can use it for a perfect disentangling among tensors. Applying a many-body decomposition recursively, we conceptually derive projected entangled pair states from quantum states that satisfy the area law of entanglement entropy. |
Thursday, March 8, 2018 1:39PM - 1:51PM |
S34.00011: Tensor Networks for Reversible Classical Computation and Time Evolution of Quantum Many-Body Systems Zhicheng Yang, Stefanos Kourtis, Claudio Chamon, Eduardo Mucciolo, Andrei Ruckenstein Motivated by statistical physics models connected to computational problems, we introduce an iterative compression-decimation scheme for tensor network optimization that is suited to problems without translation invariance and with arbitrary boundary conditions. When applied to tensor networks that encode generalized vertex models on regular lattices, our algorithm is able to propagate global constraints imposed at the boundary via repeated contraction-decomposition sweeps over all lattice bonds, followed by coarse-graining tensor contractions. We apply our algorithm to a recently proposed vertex model encoding universal reversible classical computations. Our protocol allows us to obtain the exact number of solutions for computations where a naive enumeration would take astronomically long times. We also gain insights into the hardness of a computation from an entanglement perspective. Finally, I will discuss how our algorithm can be applied to simulating unitary time evolutions in quantum many-body systems. |
Thursday, March 8, 2018 1:51PM - 2:03PM |
S34.00012: Entanglement Negativity in the Kondo Model at Finite Temperature Jeongmin Shim, Heung-Sun Sim, Seung-Sup Lee Entanglement is useful to characterize many-body ground states. It will be also interesting to study entanglement in many-body thermal states. We compute the entanglement negativity between the impurity and the bath for the single-impurity Kondo model and for the single-impurity Anderson model at finite temperature, using the numerical renormalization group method. For the Kondo model, the negativity detects the features of the low-energy Fermi-Liquid quasiparticles, such as universal power-law thermal suppression [1] of the entanglement. For the Anderson model, the negativity shows the temperature dependence which reflects the renormalization group flow of the model. |
Thursday, March 8, 2018 2:03PM - 2:15PM |
S34.00013: Entanglement entropy of quantum many-body systems from unitary disentangling flows Stefan Kehrein The Ryu-Takayanagi conjecture [1] establishes a remarkable connection between quantum systems and geometry. Specifically, it relates the entanglement entropy to minimal surfaces within the setting of AdS/CFT correspondence. I show that a unitary disentangling flow in an emergent RG-like direction permits a generalization of these ideas to generic quantum many-body Hamiltonians without requiring conformal invariance [2]. The min-entanglement entropy can be obtained in a systematic expansion around a weak-link limit where the region whose entanglement properties one is interested in is weakly coupled to the rest of the system. This formalism also allows for the calculation of subdominant terms in the entanglement entropy and for studying the crossover to volume law behavior at nonzero temperature. |
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