arXiv subjects

R. M. Noack

Publications and source records attributed to R. M. Noack.

At least 19 recordsLinked to original sources

arXiv2023

Three-qubit Deutsch-Jozsa in measurement-based quantum computing

Measurement-based quantum computing (MBQC), an alternate paradigm for formulating quantum algorithms, can lead to potentially more flexible and efficient implementations as well as to theoretical insights on the role of entanglement in a quantum algorithm. Using the graph-theoretical ZX-calculus, we describe and apply a general scheme for reformulating quantum circuits as MBQC implementations. After illustrating the method using the two-qubit Deutsch-Jozsa algorithm, we derive a ZX graph-diagram that encodes a general MBQC implementation for the three-qubit Deutsch-Jozsa algorithm. This graph describes an 11-qubit cluster state on which single-qubit measurements are used to execute the algorithm. Particular sets of choices of the axes for the measurements can be used to implement any realization of the oracle. In addition, we derive an equivalent lattice cluster state for the algorithm.

quant-ph↗

arXiv2018

Anisotropy crossover in the frustrated Hubbard model on four-chain cylinders

Motivated by dimensional crossover in layered organic $κ$ salts, we determine the phase diagram of a system of four periodically coupled Hubbard chains with frustration at half filling as a function of the interchain hopping ${t_{\perp}/t}$ and interaction strength ${U/t}$ at a fixed ratio of frustration and interchain hopping ${t'/t_{\perp}=-0.5}$. We cover the range from the one-dimensional limit of uncoupled chains (${t_{\perp}/t=0.0}$) to the isotropic model (${t_{\perp}/t=1.0}$). For strong ${U/t}$, we find an antiferromagnetic insulator; in the weak-to-moderate-interaction regime, the phase diagram features quasi-one-dimensional antiferromagnetic behavior, an incommensurate spin-density wave, and a metallic phase as ${t_{\perp}/t}$ is increased. We characterize the phases through their magnetic ordering, dielectric response, and dominant static correlations. Our analysis is based primarily on a variant of the density-matrix renormalization-group algorithm based on an efficient hybrid-real-momentum-space formulation, in which we can treat relatively large lattices albeit of a limited width. This is complemented by a variational cluster approximation study with a cluster geometry corresponding to the cylindrical lattice allowing us to directly compare the two methods for this geometry. As an outlook, we make contact with work studying dimensional crossover in the full two-dimensional system.

cond-mat.str-el↗

arXiv2017

Entanglement structure of the Hubbard model in momentum space

We study the properties of the ground states of the one- and two-dimensional Hubbard models at half filling and moderate doping using entanglement-based measures, which we calculate numerically using the momentum-space density matrix renormalization group (DMRG). In particular, we investigate quantities such as the single-site entropy and two-site mutual information of single-particle momentum states as well as the behavior of the bipartite subsystem entropy for partitions in momentum space. The distribution of these quantities in momentum space gives insight into the fundamental nature of the ground state, insight that can be used to make contact with weak-coupling-based analytic approaches and to optimize numerical methods, the momentum-space DMRG in particular. We study the site and subsystem entropies as a function of interaction strength $U$ and system size. In both the one- and two-dimensional cases, we find that the subsystem entropy scales proportionally to $U^2$ for weak $U$ and proportionally to volume. Nevertheless, the optimized momentum-space DMRG can provide variationally accurate results for the two-dimensional Hubbard model at weak coupling for moderate system sizes.

cond-mat.str-el↗

arXiv2017

Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model

The performance of the density matrix renormalization group (DMRG) is strongly influenced by the choice of the local basis of the underlying physical lattice. We demonstrate that, for the two-dimensional Hubbard model, the hybrid real-momentum space formulation of the DMRG is computationally more efficient than the standard real-space formulation. In particular, we show that the computational cost for fixed bond dimension of the hybrid-space DMRG is approximately independent of the width of the lattice, in contrast to the real-space DMRG, for which it is proportional to the width squared. We apply the hybrid-space algorithm to calculate the ground state of the doped two-dimensional Hubbard model on cylinders of width four and six sites; at $n=0.875$ filling, the ground state exhibits a striped charge-density distribution with a wavelength of eight sites for both $U/t=4.0$ and $U/t=8.0$. We find that the strength of the charge ordering depends on $U/t$ and on the boundary conditions.Furthermore, we investigate the magnetic ordering as well as the decay of the static spin, charge, and pair-field correlation functions.

cond-mat.str-el↗

arXiv2015

Entanglement patterns and generalized correlation functions in quantum many body systems

We introduce transition operators that in a given basis of the single-site states of a many-body system have a single non-vanishing matrix element and introduce their correlation functions. We show that they fall into groups that decay with the same rate. The mutual information defined in terms of the von Neumann entropy between two sites is given in terms of these so-called generalized correlation functions. We confirm numerically that the long-distance decay of the mutual information follows the square of that of the most slowly decaying generalized correlation function. The main advantage of our procedure is that, in order to identify the most relevant physical processes, there is no need to know a priori the nature of the ordering in the system, i.e., no need to explicitly construct particular physical correlation functions. We explore the behavior of the mutual information and the generalized correlation functions for conformally invariant models and for the SU($n$) Hubbard model with $n=2,3,4$, and 5, which are, in general, not conformally invariant. In this latter case, we show that for filling $f=1/q$ and $q<n$, the ground state consists of highly entangled $q$-site units that are further entangled by single bonds. In addition, we extend the picture of the two-site mutual information and the corresponding generalized correlation functions to the $n$-site case.

cond-mat.str-el↗

arXiv2011

On the dimerized phase in the cross-coupled antiferromagnetic spin ladder

We revisit the phase diagram of the frustrated s=1/2 spin ladder with antiferromagnetic rung and diagonal couplings. In particular, we reexamine the evidence for the columnar dimer phase, which has been predicted from analytic treatment of the model and has been claimed to be found in numerical calculations. By considering longer chains and by keeping more states than in previous work using the density-matrix renormalization group, we show that the numerical evidence presented previously for the existence of the dimerized phase is not unambiguous in view of the present more careful analysis. While we cannot completely rule out the possibility of a dimerized phase in the cross-coupled ladder, we do set limits on the maximum possible value of the dimer order parameter that are much smaller than those found previously.

cond-mat.str-el↗

arXiv2011

Adaptive Lanczos-vector method for dynamic properties within the density-matrix renormalization group

Current widely-used approaches to calculate spectral functions using the density-matrix renormalization group in frequency space either necessarily include an artificial broadening (correction-vector method) or have limited resolution (time-domain density-matrix renormalization group with Fourier transform method). Here we propose an adaptive Lanczos-vector method to calculate the coefficients of a continued fraction expansion of the spectral function iteratively. We show that one can obtain a very accurate representation of the spectral function very efficiently, and that one can also directly extract the spectral weights and poles for the discrete system. As a test case, we study spinless fermions in one dimension and compare our approach to the correction vector method.

cond-mat.str-el↗

arXiv2009

Quantum information analysis of the phase diagram of the half-filled extended Hubbard model

We examine the phase diagram of the half-filled one-dimensional extended Hubbard model using quantum information entropies within the density-matrix renormalization group. It is well known that there is a charge-density-wave phase at large nearest-neighbor and small on-site Coloumb repulsion and a spin-density-wave at small nearest-neighbor and large on-site Coloumb repulsion. At intermediate Coulomb interaction strength, we find an additional narrow region of a bond-order phase between these two phases. The phase transition line for the transition out of the charge-density-wave phase changes from first-order at strong coupling to second-order in a parameter regime where all three phases are present. We present evidence that the additional phase-transition line between the spin-density-wave and bond-order phases is infinite order. While these results are in agreement with recent numerical work, our study provides an independent, unbiased means of determining the phase boundaries by using quantum information analysis, yields values for the location of some of the phase boundaries that differ from those previously found, and provides insight into the limitations of numerical methods in determining phase boundaries, especially those of infinite-order transitions.

cond-mat.str-el↗

arXiv2009

Critical properties of the band-insulator-to-Mott-insulator transition in the strong-coupling limit of the ionic Hubbard model

We investigate the neutral-to-ionic insulator-insulator transition in one-dimensional materials by treating a strong-coupling effective model based on the ionic Hubbard model using the density-matrix renormalization group and finite-size scaling. The effective model, formulated in a spin-one representation, contains a single parameter. We carry out an extensive finite-size scaling analysis of the relevant gaps and susceptibilities to characterize the two zero-temperature transitions. We find that the transition from the ionic band-insulating phase to an intermediate spontaneously dimerized phase is Ising, and the transition from the dimerized phase to the Mott-insulating phase is Kosterlitz-Thouless, in agreement with the field-theory-based predictions.

cond-mat.str-el↗

arXiv2008

Random dispersion approximation for the Hubbard model

We use the Random Dispersion Approximation (RDA) to study the Mott-Hubbard transition in the Hubbard model at half band filling. The RDA becomes exact for the Hubbard model in infinite dimensions. We implement the RDA on finite chains and employ the Lanczos exact diagonalization method in real space to calculate the ground-state energy, the average double occupancy, the charge gap, the momentum distribution, and the quasi-particle weight. We find a satisfactory agreement with perturbative results in the weak- and strong-coupling limits. A straightforward extrapolation of the RDA data for $L\leq 14$ lattice results in a continuous Mott-Hubbard transition at $U_{\rm c}\approx W$. We discuss the significance of a possible signature of a coexistence region between insulating and metallic ground states in the RDA that would correspond to the scenario of a discontinuous Mott-Hubbard transition as found in numerical investigations of the Dynamical Mean-Field Theory for the Hubbard model.

cond-mat.str-el↗

arXiv2008

Magnetism of one-dimensional Wigner lattices and its impact on charge order

The magnetic phase diagram of the quarter-filled generalized Wigner lattice with nearest- and next-nearest-neighbor hopping t_1 and t_2 is explored. We find a region at negative t_2 with fully saturated ferromagnetic ground states that we attribute to kinetic exchange. Such interaction disfavors antiferromagnetism at t_2 <0 and stems from virtual excitations across the charge gap of the Wigner lattice, which is much smaller than the Mott-Hubbard gap proportional to U. Remarkably, we find a strong dependence of the charge structure factor on magnetism even in the limit U to infinity, in contrast to the expectation that charge ordering in the Wigner lattice regime should be well described by spinless fermions. Our results, obtained using the density-matrix renormalization group and exact diagonalization, can be transparently explained by means of an effective low-energy Hamiltonian.

cond-mat.str-el↗

arXiv2008

Phase diagram of the t-U-J1-J2 chain at half filling

We investigate the half-filled Hubbard chain with additional nearest- and next-nearest-neighbor spin exchange, J1 and J2, using bosonization and the density-matrix renormalization group. For J2 = 0 we find a spin-density-wave phase for all positive values of the Hubbard interaction U and the Heisenberg exchange J1. A frustrating spin exchange J2 induces a bond-order-wave phase. For some values of J1, J2 and U, we observe a spin-gapped metallic Luther-Emery phase.

cond-mat.str-el↗

arXiv2008

The ALPS project release 1.3: open source software for strongly correlated systems

We present release 1.3 of the ALPS (Algorithms and Libraries for Physics Simulations) project, an international open source software project to develop libraries and application programs for the simulation of strongly correlated quantum lattice models such as quantum magnets, lattice bosons, and strongly correlated fermion systems. Development is centered on common XML and binary data formats, on libraries to simplify and speed up code development, and on full-featured simulation programs. The programs enable non-experts to start carrying out numerical simulations by providing basic implementations of the important algorithms for quantum lattice models: classical and quantum Monte Carlo (QMC) using non-local updates, extended ensemble simulations, exact and full diagonalization (ED), as well as the density matrix renormalization group (DMRG). Changes in the new release include a DMRG program for interacting models, support for translation symmetries in the diagonalization programs, the ability to define custom measurement operators, and support for inhomogeneous systems, such as lattice models with traps. The software is available from our web server at http://alps.comp-phys.org/ .

cond-mat.str-el↗

arXiv2007

Strongly correlated fermions after a quantum quench

Using the adaptive time-dependent density-matrix renormalization group method, we study the time evolution of strongly correlated spinless fermions on a one-dimensional lattice after a sudden change of the interaction strength. For certain parameter values, two different initial states (e.g., metallic and insulating), lead to observables which become indistinguishable after relaxation. We find that the resulting quasi-stationary state is non-thermal. This result holds for both integrable and non-integrable variants of the system.

cond-mat.other↗

arXiv2006

Uniform and staggered magnetizations induced by Dzyaloshinskii-Moriya interactions in isolated and coupled spin 1/2 dimers in a magnetic field

We investigate the interplay of Dzyaloshinskii-Moriya interactions and an external field in spin 1/2 dimers. For isolated dimers and at low field, we derive simple expressions for the staggered and uniform magnetizations which show that the orientation of the uniform magnetization can deviate significantly from that of the external field. In fact, in the limit where the ${\bf D}$ vector of the Dzyaloshinskii-Moriya interaction is parallel to the external field, the uniform magnetization actually becomes {\it perpendicular} to the field. For larger fields, we show that the staggered magnetization of an isolated dimer has a maximum close to one-half the polarization, with a large maximal value of $0.35 gμ_B$ in the limit of very small Dzyaloshinskii-Moriya interaction. We investigate the effect of inter-dimer coupling in the context of ladders with Density Matrix Renormalization Group (DMRG) calculations and show that, as long as the values of the Dzyaloshinskii-Moriya and of the exchange interaction are compatible with respect to the development of a staggered magnetization, the simple picture that emerges for isolated dimers is also valid for weakly coupled dimers with minor modifications. The results are compared with torque measurements on Cu$_{2}$(C$_{5}$H$_{12}$N$_{2}$)$_{2}$Cl$_{4}$.

cond-mat.str-el↗

arXiv2006

Entropic analysis of quantum phase transitions from uniform to spatially inhomogeneous phases

We propose a new approach to study quantum phase transitions in low-dimensional fermionic or spin models that go from uniform to spatially inhomogeneous phases such as dimerized, trimerized, or incommensurate phases. It is based on studying the length dependence of the von Neumann entropy and its corresponding Fourier spectrum for finite segments in the ground state of finite chains. Peaks at a nonzero wave vector are indicators of oscillatory behavior in decaying correlation functions.

cond-mat.str-el↗

arXiv2006

Coherent matter waves emerging from Mott-insulators

We study the formation of (quasi-)coherent matter waves emerging from a Mott insulator for strongly interacting bosons on a one-dimensional lattice. It has been shown previously that a quasi-condensate emerges at momentum k=π/2a, where a is the lattice constant, in the limit of infinitely strong repulsion (hard-core bosons). Here we show that this phenomenon persists for all values of the repulsive interaction that lead to a Mott insulator at a commensurate filling. The non-equilibrium dynamics of hard-core bosons is treated exactly by means of a Jordan-Wigner transformation, and the generic case is studied using a time-dependent density matrix renormalization group technique. Different methods for controlling the emerging matter wave are discussed.

cond-mat.other↗

arXiv2006

Nature of the metal-insulator transition in the half--filled t-t' Hubbard chain

We study the quantum phase transition from an insulator to a metal realized at t'=t'_c > 0.5t in the ground state of the half-filled Hubbard chain with both nearest-neighbor (t) and next-nearest-neighbor (t') hopping. The study is carried out using the bosonization approach and density matrix renormalization group calculations. An effective low-energy Hamiltonian that describes the insulator-metal transition is derived. We find that the gross features of the phase diagram are well-described by the standard theory of commensurate-incommensurate transitions in a wide range of parameters. We also obtain an analytical expression for the insulator-metal transition line t'_c(U,t). We argue that close to the insulator-metal transition line, a crossover to a regime corresponding to an infinite-order transition takes place.We present results of density-matrix-renormalization-group calculations of spin and charge distribution in various sectors of the phase diagram. The numerical results support the picture derived from the effective theory and give evidence for the complete separation of the transitions involving spin and charge degrees of freedom.

cond-mat.str-el↗