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 WitczakKrempa, 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 wellknown that ground states of gapped onedimensional (1d) quantummany body systems with shortrange 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 groundstate representation using adiabatic optimization. The basic idea follows the socalled ssource 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, WenYuan Liu, ShaoJun Dong, YongJian Han, GC Guo The projected entangled pair states (PEPS) methods have been proved to be powerful tools to solve the strongly correlated quantum manybody problems in twodimension. 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 J_{1}J_{2 }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 KooSaleur 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 KooSaleur 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 lowenergy excited states of the circular critical spin chain appear to be well captured by the Blochstate 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 BetheAnsatz states of the XXZ spin1/2 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 spinflips considered would have been doubled. Our method is generic for any nonnested integrable model, and we show this by deriving a matrix product representation of the Bethe eigenstates of the LiebLiniger 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 manybody 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 doublelog leadingorder correction. By employing the correlation matrix method, we illustrate our theoretical findings in systems of up to 10^{5} particles. 
Thursday, March 8, 2018 1:03PM  1:15PM 
S34.00008: Operational entanglement of interacting spinless fermions in onedimension Adrian Del Maestro, Hatem Barghathi, Emanuel CasianoDiaz For indistinguishable itinerant particles subject to a superselection 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 TomonagaLuttinger 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 firstorder 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 onedimensional or quasionedimensional quantum manybody systems. However, there can be situations that are particularly challenging for DMRG to solve owing to its local optimization procedure. One such example are firstorder 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 lowlying 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 firstorder 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 manybody 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 higherorder 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 manybody decomposition of a tensor by using an entanglement branching operator. We can use it for a perfect disentangling among tensors. Applying a manybody 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 ManyBody Systems Zhicheng Yang, Stefanos Kourtis, Claudio Chamon, Eduardo Mucciolo, Andrei Ruckenstein Motivated by statistical physics models connected to computational problems, we introduce an iterative compressiondecimation 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 contractiondecomposition sweeps over all lattice bonds, followed by coarsegraining 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 manybody systems. 
Thursday, March 8, 2018 1:51PM  2:03PM 
S34.00012: Entanglement Negativity in the Kondo Model at Finite Temperature Jeongmin Shim, HeungSun Sim, SeungSup Lee Entanglement is useful to characterize manybody ground states. It will be also interesting to study entanglement in manybody thermal states. We compute the entanglement negativity between the impurity and the bath for the singleimpurity Kondo model and for the singleimpurity Anderson model at finite temperature, using the numerical renormalization group method. For the Kondo model, the negativity detects the features of the lowenergy FermiLiquid quasiparticles, such as universal powerlaw 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 manybody systems from unitary disentangling flows Stefan Kehrein The RyuTakayanagi 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 RGlike direction permits a generalization of these ideas to generic quantum manybody Hamiltonians without requiring conformal invariance [2]. The minentanglement entropy can be obtained in a systematic expansion around a weaklink 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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