Density Matrix Renormalization Group for Dummies

We describe the Density Matrix Renormalization Group algorithms for time dependent and time independent Hamiltonians. This paper is a brief but comprehensive introduction to the subject for anyone willing to enter in the field or write the program source code from scratch. An open source version of the code can be found at: http://www.dmrg.it.

Strong electronic correlation in the hydrogen chain: A variational Monte Carlo study

In this paper, we report a fully ab initio variational Monte Carlo study of the linear and periodic chain of hydrogen atoms, a prototype system providing the simplest example of strong electronic correlation in low dimensions. In particular, we prove that numerical accuracy comparable to that of benchmark density-matrix renormalization-group calculations can be achieved by using a highly correlated Jastrow-antisymmetrized geminal power variational wave function. Furthermore, by using the so-called "modern theory of polarization" and by studying the spin-spin and dimer-dimer correlations functions, we have characterized in detail the crossover between the weakly and strongly correlated regimes of this atomic chain. Our results show that variational Monte Carlo provides an accurate and flexible alternative to highly correlated methods of quantum chemistry which, at variance with these methods, can be also applied to a strongly correlated solid in low dimensions close to a crossover or a phase transition.

Entanglement entropy dynamics of Heisenberg chains

By means of the time dependent density matrix renormalization group algorithm we study the zero-temperature dynamics of the Von Neumann entropy of a block of spins in a Heisenberg chain after a sudden quench in the anisotropy parameter. In the absence of any disorder the block entropy increases linearly with time and then saturates. We analyse the velocity of propagation of the entanglement as a function of the initial and final anisotropies and compare our results, wherever possible, with those obtained by means of conformal field theory. In the disordered case we find a slower ( logarithmic) evolution which may signal the onset of entanglement localization.

Phase diagram of spin-1 bosons on one-dimensional lattices

Spinor Bose condensates loaded in optical lattices have a rich phase diagram characterized by different magnetic order. Here we apply the density matrix renormalization group to accurately determine the phase diagram for spin-1 bosons loaded on a one-dimensional lattice. The Mott lobes present an even or odd asymmetry associated to the boson filling. We show that for odd fillings the insulating phase is always in a dimerized state. The results obtained in this work are also relevant for the determination of the ground state phase diagram of the S=1 Heisenberg model with biquadratic interaction.

Bilinear-biquadratic spin-1 chain undergoing quadratic Zeeman effect

The Heisenberg model for spin-1 bosons in one dimension presents many different quantum phases, including the famous topological Haldane phase. Here we study the robustness of such phases in front of a SU(2) symmetry-breaking field as well as the emergence of unique phases. Previous studies have analyzed the effect of such uniaxial anisotropy in some restricted relevant points of the phase diagram. Here we extend those studies and present the complete phase diagram of the spin-1 chain with uniaxial anisotropy. To this aim, we employ the density-matrix renormalization group together with analytical approaches. The complete phase diagram can be realized using ultracold spinor gases in the Mott insulator regime under a quadratic Zeeman effect.

Scaling of the entanglement spectrum near quantum phase transitions

The entanglement spectrum describing quantum correlations in many-body systems has been recently recognized as a key tool to characterize different quantum phases, including topological ones. Here we derive its analytically scaling properties in the vicinity of some integrable quantum phase transitions and extend our studies also to nonintegrable quantum phase transitions in one-dimensional spin models numerically. Our analysis shows that, in all studied cases, the scaling of the difference between the two largest nondegenerate Schmidt eigenvalues yields with good accuracy critical points and mass scaling exponents.

Full characterization of the quantum linear-zigzag transition in atomic chains

A string of repulsively interacting particles exhibits a phase transition to a zigzag structure, by reducing the transverse trap potential or the interparticle distance. Based on the emergent symmetry Z2 it has been argued that this instability is a quantum phase transition, which can be mapped to an Ising model in transverse field. An extensive Density Matrix Renormalization Group analysis is performed, resulting in an high-precision evaluation of the critical exponents and of the central charge of the system, confirming that the quantum linear-zigzag transition belongs to the critical Ising model universality class. Quantum corrections to the classical phase diagram are computed, and the range of experimental parameters where quantum effects play a role is provided. These results show that structural instabilities of one-dimensional interacting atomic arrays can simulate quantum critical phenomena typical of ferromagnetic systems.

Nonequilibrium critical scaling from quantum thermodynamics

The emerging field of quantum thermodynamics is contributing important results and insights into archetypal many-body problems, including quantum phase transitions. Still, the question whether out-of-equilibrium quantities, such as fluctuations of work, exhibit critical scaling after a sudden quench in a closed system has remained elusive. Here, we take a novel approach to the problem by studying a quench across an impurity quantum critical point. By performing density matrix renormalization group computations on the two-impurity Kondo model, we are able to establish that the irreversible work produced in a quench exhibits finite-size scaling at quantum criticality. This scaling faithfully predicts the equilibrium critical exponents for the crossover length and the order parameter of the model, and, moreover, implies a new exponent for the rescaled irreversible work. By connecting the irreversible work to the two-impurity spin correlation function, our findings can be tested experimentally.

Failure of a numerical quality assessment scale to identify potential risk of bias in a systematic review: a comparison study

BACKGROUND: Assessing methodological quality of primary studies is an essential component of systematic reviews. Following a systematic review which used a domain based system [United States Preventative Services Task Force (USPSTF)] to assess methodological quality, a commonly used numerical rating scale (Downs and Black) was also used to evaluate the included studies and comparisons were made between quality ratings assigned using the two different methods. Both tools were used to assess the 20 randomized and quasi-randomized controlled trials examining an exercise intervention for chronic musculoskeletal pain which were included in the review. Inter-rater reliability and levels of agreement were determined using intraclass correlation coefficients (ICC). Influence of quality on pooled effect size was examined by calculating the between group standardized mean difference (SMD).

RESULTS: Inter-rater reliability indicated at least substantial levels of agreement for the USPSTF system (ICC 0.85; 95% CI 0.66, 0.94) and Downs and Black scale (ICC 0.94; 95% CI 0.84, 0.97). Overall level of agreement between tools (ICC 0.80; 95% CI 0.57, 0.92) was also good. However, the USPSTF system identified a number of studies (n = 3/20) as "poor" due to potential risks of bias. Analysis revealed substantially greater pooled effect sizes in these studies (SMD -2.51; 95% CI -4.21, -0.82) compared to those rated as "fair" (SMD -0.45; 95% CI -0.65, -0.25) or "good" (SMD -0.38; 95% CI -0.69, -0.08).

CONCLUSIONS: In this example, use of a numerical rating scale failed to identify studies at increased risk of bias, and could have potentially led to imprecise estimates of treatment effect. Although based on a small number of included studies within an existing systematic review, we found the domain based system provided a more structured framework by which qualitative decisions concerning overall quality could be made, and was useful for detecting potential sources of bias in the available evidence.

Comprehensive numerical modelling of the performance of a second harmonic generation stage coupled with a low-gain optical parametric amplifier

We present a comprehensive model for predicting the full performance of a second harmonic generation-optical parametric amplification system that aims at enhancing the temporal contrast of laser pulses. The model simultaneously takes into account all the main parameters at play in the system such as the group velocity mismatch, the beam divergence, the spectral content, the pump depletion, and the length of the nonlinear crystals. We monitor the influence of the initial parameters of the input pulse and the interdependence of the two related non-linear processes on the performance of the system and show its optimum configuration. The influence of the initial beam divergence on the spectral and the temporal characteristics of the generated pulse is discussed. In addition, we show that using a crystal slightly longer than the optimum length and introducing small delay between the seed and the pump ensures maximum efficiency and compensates for the spectral shift in the optical parametric amplification stage in case of chirped input pulse. As an example, calculations for bandwidth transform limited and chirped pulses of sub-picosecond duration in beta barium borate crystal are presented.