String Correlation Functions Research Articles

Correlation functions for open strings and chaos

We study the holographic interpretation of the bulk instability, i.e. the bulk Lyapunov exponent in the motion of open classical bosonic strings in AdS black hole/brane/string backgrounds. In the vicinity of homogeneous and isotropic horizons the bulk Lyapunov exponent saturates the MSS chaos bound but in fact has nothing to do with chaos as our string configurations live in an integrable sector. In the D1-D5-p black string background, the bulk Lyapunov exponent is deformed away from the MSS value both by the rotation (the infrared deformation) and the existence of an asymptotically flat region (the ultraviolet deformation). The dynamics is still integrable and has nothing to do with chaos (either in gravity or in field theory). Instead, the bulk Lyapunov scale captures the imaginary part of quasinormal mode frequencies. Therefore, the meaning of the bulk chaos is that it determines the thermal decay rate due to the coupling to the heat bath, i.e. the horizon.

Interacting second-order topological insulators in one-dimensional fermions with correlated hopping

Higher-order topological crystalline phases in low-dimensional interacting quantum systems represent a challenging and largely unexplored research topic. Here, we derive a Hamiltonian describing fermions interacting through correlated hopping processes that break chiral invariance, but preserve both inversion and time-reversal symmetries. In this way, we show that our one-dimensional model gives rise to an interacting second-order topological insulating phase that supports gapped edge states. The topological nature of such interacting phase turns out to be revealed by both long-range order of a non-local string correlation function and by even degeneracy of the entanglement spectrum. For strong interactions we instead find that the topological crystalline phase is destroyed and replaced by a singlet superconducting phase. The latter, characterized by local fermionic pairing, turns out to appear both in a homogeneous and in a phase separated form. Relevantly, the derived one-dimensional model and the second-order topological insulator can be explored and investigated in atomic quantum simulators.

Revealing the topological nature of the bond order wave in a strongly correlated quantum system

We investigate the topological properties of the bond order wave phase arising in the extended Fermi-Hubbard model. In particular, we uncover a topological sector, which remained elusive in previous finite-size numerical studies due to boundary effects. We first show that, for an infinite system, the bond order wave regime is characterized by two degenerate bulk states corresponding to the trivial and topological sectors. The latter turns out to be indeed characterized by an even degeneracy of the entanglement spectrum and long-range order of a string correlation function. For finite-size systems, we show that the topological sector can be stabilized by imposing a suitable border potential. This therefore provides a concrete protocol for the observation of topologically protected degenerate edge modes in finite-size systems. Furthermore, we show that the bulk of the system is characterized by exotic solitonic solutions interpolating between the trivial and topological sectors. Finally, we propose an implementation and detection scheme of this strongly correlated topological phase in a quantum simulator based on dipolar Fermi gases in optical lattices.Received 13 January 2022Revised 19 April 2022Accepted 14 June 2022DOI:https://doi.org/10.1103/PhysRevResearch.4.L032005Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCold gases in optical latticesDipolar gasesSymmetry protected topological statesTechniquesDensity matrix renormalization groupExtended Hubbard modelAtomic, Molecular & Optical

Topological Quantum Critical Points in the Extended Bose-Hubbard Model.

The combination of topology and quantum criticality can give rise to an exotic mix of counterintuitive effects. Here, we show that unexpected topological properties take place in a paradigmatic strongly correlated Hamiltonian: the 1D extended Bose-Hubbard model. In particular, we reveal the presence of two distinct topological quantum critical points with localized edge states and gapless bulk excitations. Our results show that the topological critical points separate two phases, one topologically protected and the other topologically trivial, both characterized by a long-range ordered string correlation function. The long-range order persists also at the topological critical points and explains the presence of localized edge states protected by a finite charge gap. Finally, we introduce a superresolution quantum gas microscopy scheme for dipolar dysprosium atoms, which provides a reliable route towards the experimental study of topological quantum critical points.

Correlation functions of symmetric orbifold from AdS3 string theory

The paper examines correspondence among correlation functions of symmetric orbifold and string theory on AdS3 described by sl(2) Wess-Zumino-Novikov-Witten (WZNW) model. We start by writing down n-point function of twist operators in the symmetric orbifold in terms of the data of effective Riemann surface. It is then shown that the correlation function can be reproduced from the sl(2) WZNW model. The computation is based on the claim that string worldsheet is given by the same Riemann surface and the reduction method from sl(2) WZNW model to Liouville field theory. We first consider the genus zero surface and then generalize the analysis to the case of generic genus. The radius of AdS3 is related to the level k of the WZNW model. For k = 3, our result should be an important ingredient for deriving AdS3/CFT2 correspondence with tensionless superstrings to all orders in string perturbation theory. For generic k, relations involving specific forms of correlation functions for strings on AdS3× X were obtained.

Quantum phases of a one-dimensional Majorana-Bose-Hubbard model

Majorana zero modes (MZM-s) occurring at the edges of a 1D, p-wave, spinless superconductor, in absence of fluctuations of the phase of the superconducting order parameter, are quintessential examples of topologically-protected zero-energy modes occurring at the edges of 1D symmetry-protected topological phases. In this work, we numerically investigate the fate of the topological phase in the presence of phase-fluctuations using the density matrix renormalization group (DMRG) technique. To that end, we consider a one-dimensional array of MZM-s on mesoscopic superconducting islands at zero temperature. Cooper-pair and MZM-assisted single-electron tunneling, together with finite charging energy of the mesoscopic islands, give rise to a rich phase-diagram of this model. We show that the system can be in either a Mott-insulating phase, a Luttinger liquid (LL) phase of Cooper-pairs or a second gapless phase. In contrast to the LL of Cooper-pairs, this second phase is characterized by nonlocal string correlation functions which decay algebraically due to gapless charge-$e$ excitations. The three phases are separated from each other by phase-transitions of either Kosterlitz-Thouless or Ising type. Using a Jordan-Wigner transformation, we map the system to a generalized Bose-Hubbard model with two types of hopping and use DMRG to analyze the different phases and the phase-transitions.

Infinite cascades of phase transitions in the classical Ising chain.

We report exact results on one of the best studied models in statistical physics: the classical antiferromagnetic Ising chain in a magnetic field. We show that the model possesses an infinite cascade of thermal phase transitions (also known as disorder lines or geometric phase transitions). The phase transition is signaled by a change of asymptotic behavior of the nonlocal string-string correlation functions when their monotonic decay becomes modulated by incommensurate oscillations. The transitions occur for rarefied (m-periodic) strings with arbitrary odd m. We propose a duality transformation which maps the Ising chain onto the m-leg Ising tube with nearest-neighbor couplings along the legs and the plaquette four-spin interactions of adjacent legs. Then the m-string correlation functions of the Ising chain are mapped onto the two-point spin-spin correlation functions along the legs of the m-leg tube. We trace the origin of these cascades of phase transitions to the lines of the Lee-Yang zeros of the Ising chain in m-periodic complex magnetic field, allowing us to relate these zeros to the observable (and potentially measurable) quantities.

A proposal for (0,2) mirrors of toric varieties

In this paper we propose (0,2) mirrors for general Fano toric varieties with special tangent bundle deformations, corresponding to subsets of toric deformations. Our mirrors are of the form of (B/2-twisted) (0,2) Landau-Ginzburg models, matching Hori-Vafa mirrors on the (2,2) locus. We compare our predictions to (0,2) mirrors obtained by Chen et al. for certain examples of toric varieties, and find that they match. We also briefly outline conjectures for analogous results for hypersurfaces in Fano toric varieties. Our methods utilize results from supersymmetric localization, which allows us to incidentally gain occasional further insights into GLSM-based (2,2) mirror constructions. For example, we explicitly verify that closed string correlation functions of the original A-twisted GLSM match those of the mirror B-twisted Landau-Ginzburg model, as well as (0,2) deformations thereof.

Ambitwistor strings and reggeon amplitudes in [formula omitted] SYM

We consider the description of reggeon amplitudes (Wilson lines form factors) in N=4 SYM within the framework of four dimensional ambitwistor string theory. The latter is used to derive scattering equations representation for reggeon amplitudes with multiple reggeized gluons present. It is shown, that corresponding tree-level string correlation function correctly reproduces previously obtained Grassmannian integral representation of reggeon amplitudes in N=4 SYM.

Topological Quantum Phase Transitions in a Majorana Chain with Spatial Modulation

We numerically study the quantum phase transitions and the stability of Majorana zero modes in a generalized Kitaev model in one dimension when the chemical potential is periodically modulating in space. By using the exact diagonalization method for open boundary condition, we investigate the ground-state phases in terms of the non-local properties such as the entanglement spectrum (ES) and the string correlation functions. When we vary the phase of the modulation, the number of the Majorana zero modes changes, which manifests itself in the degeneracy of the lowest level of the ES. Next, we study the quantum phase transitions driven by the change in the amplitude of the modulation. In particular, for certain values of the wave number and the phase of the modulation, we observe a quantum phase transition from one topological phase into another where the string correlation function oscillates in space. We also show a case where the degeneracy of the ES does not change even for large enough amplitude of the modulation. Finally, we characterize the phases of the system with periodic boundary condition by the topological invariant, which reflects the number of the zero-energy excitations.

Phase Diagram and Sweep Dynamics of a One-Dimensional Generalized Cluster Model

We numerically study quantum phase transitions and dynamical properties in the one-dimensional cluster model with several interactions by using the time-evolving block decimation method for infinite systems and the exact diagonalization. First, boundaries among several quantum phases of the model are determined from energy gap and each phase is characterized by order parameters and the entanglement spectrum (ES). We confirm that in the model with open boundary condition the degeneracy of the lowest levels in the ES corresponds to that of the ground states. Then, using the time-dependent Bogoliubov transformation with open boundary condition, we investigate dynamical properties during an interaction sweep through the critical point which separates two topological phases involving four-fold degeneracy in the ground state. After a slow sweep across the critical point, we observe spatially periodic structures in the string correlation functions and the entanglement entropy. It is shown that the periodicities stem from the Bogoliubov quasiparticles generated near the critical point.

Wave functions and correlation functions for GKP strings from integrability

We develop a general method of computing the contribution of the vertex operators to the semi-classical correlation functions of heavy string states, based on the state-operator correspondence and the integrable structure of the system. Our method requires only the knowledge of the local behavior of the saddle point configuration around each vertex insertion point and can be applied to cases where the precise forms of the vertex operators are not known. As an important application, we compute the contributions of the vertex operators to the three-point functions of the large spin limit of the Gubser-Klebanov-Polyakov (GKP) strings in AdS 3 spacetime, left unevaluated in our previous work [ arXiv:1110.3949 ] which initiated such a study. Combining with the finite part of the action already computed previously and with the newly evaluated divergent part of the action, we obtain finite three-point functions with the expected dependence of the target space boundary coordinates on the dilatation charge and the spin.

A light-cone approach to three-point functions in AdS5 × S5

We consider worldsheet correlation functions for strings in AdS_5 x S^5 using a light-cone gauge for the worldsheet theory. We compute the saddle-point approximation to three-point functions of BMN vertex operators, all with large charges, by explicitly finding the intersection of three euclidean BMN strings. We repeat this calculation for non-BPS circular winding strings extended along a great circle of the S^5, though in this case the appropriate form of the vertex operator is uncertain. Furthermore, we compute the spectrum of fluctuations about euclidean BMN strings for generic boundary conditions, and show that the spectrum depends only on the total charge and not the details of the string configuration. We extend our considerations to include near-BMN vertex operators and through the evaluation of the string path integral make contact with the light-cone string field theory calculations of gauge theory three-point structure constants.

Holographic correlation functions for open strings and branes

In this paper, we compute holographically the two-point and three-point functions of giant gravitons with open strings. We consider the maximal giant graviton in S 5 and the string configurations corresponding to the ground states of Z = 0 and Y = 0 open spin chain, and the spinning string in AdS5 corresponding to the derivative type impurities in Y = 0 or Z = 0 open spin chain as well. We treat the D-brane and open string contribution separately and find the corresponding D3-brane and string configurations in bulk which connect the composite operators at the AdS5 boundary. We apply a new prescription to treat the string state contribution and find agreements for the two-point functions. For the three-point functions of two giant gravitons with open strings and one certain half-BPS chiral primary operator, we find that the D-brane contributions to structure constant are always vanishing and the open string contribution for the Y = 0 ground state is in perfect match with the prediction in the free field limit.

Calculation of string correlation functions on a hierarchical tree

String correlation functions in 2D gravity resemble similar objects in the statisticalmechanics of directed polymer models on disordered trees. This analogy can be used toprovide an approximate mapping between the two problems. Using such a mapping wederive renormalization group equations and calculate the ensuing scaling of the stringcorrelation functions. We find it to agree with the results known for 2D gravity. The resultfurther substantiates the similarity between the two models and shows that they share notonly the free energy in the thermodynamic limit but also the gross structure of thecorrelation functions.

Finite-size scaling of string order parameters characterizing the Haldane phase

We have developed a numerical procedure to clarify the critical behavior near a quantum phase transition by analyzing a multipoint correlation function characterizing the ground state. This work presents a successful application of this procedure to the string order parameter of the $S=1$ $XXZ$ chain with uniaxial single-ion anisotropy. The finite-size string correlation function is estimated by the density-matrix renormalization-group method. We focus on the gradient of the inverse-system-size dependence of the correlation function on a logarithmic plot. This quantity shows that the finite-size scaling sensitively changes at the critical point. The behavior of the gradient with increasing system size is divergent, is stable at a finite value, or rapidly decreases to zero when the system is in the disordered phase, at the critical point, or in the ordered phase, respectively. The analysis of the finite-size string correlation functions allows precise determination of the boundary of the Haldane phase and estimation of the critical exponent of the correlation length. Our estimates of the transition point and the critical exponents, which are determined only by the ground-state quantities, are consistent with results obtained from the analysis of the energy-level structure. Our analysis requires only the correlation functions of several finite sizes under the same condition as a candidate for the long-range order. The quantity is treated in the same manner irrespective of the kind of elements which destroy the order concerned. This work will assist in the development of a method for directly observing quantum phase transitions.

String correlation functions of the spin-1/2 Heisenberg XXZ chain

We calculate certain string correlation functions, originally introduced as order parameters in integer spin chains, for the spin-1/2 XXZ Heisenberg chain at zero temperature and in the thermodynamic limit. For small distances, we obtain exact results from Bethe Ansatz and exact diagonalization, whereas in the large-distance limit, field-theoretical arguments yield an asymptotic algebraic decay. We also make contact with two-point spin-correlation functions in the asymptotic limit.

Recursive structures in string field theory

We derive recursion relations for closed string correlation functions and scattering amplitudes which hold to all orders in perturbation theory.

Quantum global vortex strings in a background field

We consider quantum global vortex string correlation functions, within the Kalb-Ramond framework, in the presence of a background field-strength tensor and investigate the conditions under which this yields a nontrivial contribution to those correlation functions. We show that a background field must be supplemented to the Kalb-Ramond theory, in order to correctly describe the quantum properties of the vortex strings. The explicit form of this background field and the associated quantum vortex string correlation function are derived. The complete expression for the quantum vortex creation operator is explicitly obtained. We discuss the potential applicability of our results in the physics of superfluids and rotating Bose-Einstein condensates.

Numerical evidence of a spin-1∕2chain approaching a spin-1 chain

In this article, we study the one dimensional Heisenberg spin-1/2 alternating bond chain in which the nearest neighbor exchange couplings are ferromagnetic (FM) and antiferromagnetic (AF) alternatively. By using exact diagonalization and density matrix renormalization groups (DMRG) method, we discuss how the system approaches to the AF uniform spin-1 chain under certain condition. When the ratio of AF to FM coupling strength}$\alpha$ $(\alpha=J_{AF}/J_{F})$ \textit{is very small, the physical quantities of the alternating bond chain such as the spin-spin correlation, the string correlation function and the spin density coincide with that of the AF uniform spin-1 chain. The edge state problem is discussed in the present model with small}$\alpha$\textit{limit. In addition, the Haldane gap of the AF uniform spin-1 chain is 4-times of the gap of the system considered.