arXiv subjects

Hana Saito

Publications and source records attributed to Hana Saito.

7 recordsLinked to original sources

arXiv2016

Towards overcoming the Monte Carlo sign problem with tensor networks

The study of lattice gauge theories with Monte Carlo simulations is hindered by the infamous sign problem that appears under certain circumstances, in particular at non-zero chemical potential. So far, there is no universal method to overcome this problem. However, recent years brought a new class of non-perturbative Hamiltonian techniques named tensor networks, where the sign problem is absent. In previous work, we have demonstrated that this approach, in particular matrix product states in 1+1 dimensions, can be used to perform precise calculations in a lattice gauge theory, the massless and massive Schwinger model. We have computed the mass spectrum of this theory, its thermal properties and real-time dynamics. In this work, we review these results and we extend our calculations to the case of two flavours and non-zero chemical potential. We are able to reliably reproduce known analytical results for this model, thus demonstrating that tensor networks can tackle the sign problem of a lattice gauge theory at finite density.

hep-lat↗

arXiv2016

The multi-flavor Schwinger model with chemical potential - Overcoming the sign problem with Matrix Product States

During recent years there has been an increasing interest in the application of matrix product states, and more generally tensor networks, to lattice gauge theories. This non-perturbative method is sign problem free and has already been successfully used to compute mass spectra, thermal states and phase diagrams, as well as real-time dynamics for Abelian and non-Abelian gauge models. In previous work we showed the suitability of the method to explore the zero-temperature phase structure of the multi-flavor Schwinger model at non-zero chemical potential, a regime where the conventional Monte Carlo approach suffers from the sign problem. Here we extend our numerical study by looking at the spatially resolved chiral condensate in the massless case. We recover spatial oscillations, similar to the theoretical predictions for the single-flavor case, with a chemical potential dependent frequency and an amplitude approximately given by the homogeneous zero density condensate value.

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arXiv2016

Chiral condensate in the Schwinger model with Matrix Product Operators

Tensor network (TN) methods, in particular the Matrix Product States (MPS) ansatz, have proven to be a useful tool in analyzing the properties of lattice gauge theories. They allow for a very good precision, much better than standard Monte Carlo (MC) techniques for the models that have been studied so far, due to the possibility of reaching much smaller lattice spacings. The real reason for the interest in the TN approach, however, is its ability, shown so far in several condensed matter models, to deal with theories which exhibit the notorious sign problem in MC simulations. This makes it prospective for dealing with the non-zero chemical potential in QCD and other lattice gauge theories, as well as with real-time simulations. In this paper, using matrix product operators, we extend our analysis of the Schwinger model at zero temperature to show the feasibility of this approach also at finite temperature. This is an important step on the way to deal with the sign problem of QCD. We analyze in detail the chiral symmetry breaking in the massless and massive cases and show that the method works very well and gives good control over a broad range of temperatures, essentially from zero to infinite temperature.

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arXiv2014

The temperature dependence of the chiral condensate in the Schwinger model with Matrix Product States

We present our recent results for the tensor network (TN) approach to lattice gauge theories. TN methods provide an efficient approximation for quantum many-body states. We employ TN for one dimensional systems, Matrix Product States, to investigate the 1-flavour Schwinger model. In this study, we compute the chiral condensate at finite temperature. From the continuum extrapolation, we obtain the chiral condensate in the high temperature region consistent with the analytical calculation by Sachs and Wipf.

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arXiv2013

Matrix Product States for Lattice Field Theories

The term Tensor Network States (TNS) refers to a number of families of states that represent different ansätze for the efficient description of the state of a quantum many-body system. Matrix Product States (MPS) are one particular case of TNS, and have become the most precise tool for the numerical study of one dimensional quantum many-body systems, as the basis of the Density Matrix Renormalization Group method. Lattice Gauge Theories (LGT), in their Hamiltonian version, offer a challenging scenario for these techniques. While the dimensions and sizes of the systems amenable to TNS studies are still far from those achievable by 4-dimensional LGT tools, Tensor Networks can be readily used for problems which more standard techniques, such as Markov chain Monte Carlo simulations, cannot easily tackle. Examples of such problems are the presence of a chemical potential or out-of-equilibrium dynamics. We have explored the performance of Matrix Product States in the case of the Schwinger model, as a widely used testbench for lattice techniques. Using finite-size, open boundary MPS, we are able to determine the low energy states of the model in a fully non-perturbative manner and to accurately extract the mass spectrum. In this work we extend the analysis to the determination of the chiral condensate, both for massless and massive fermions. The method allows for accurate finite size and continuum limit extrapolations and produces remarkably precise results, thus showing the feasibility of these techniques for gauge theory problems.

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arXiv2012

Phase structure of finite density QCD with a histogram method

We study the phase structure of QCD in the $T-μ$ plane using a histogram method and the reweighting technique by performing phase quenched simulations of two-flavor QCD with RG-improved gauge action and O($a$) improved Wilson quark action. Taking the effects of the complex phase of the quark determinant using the cumulant expansion method, we calculate the probability distribution function of plaquette and phase-quenched determinant as a function of $T$ and $μ$. We discuss the order of the QCD phase transition consulting the shape of the probability distribution function.

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arXiv2012

Numerical study of QCD phase diagram at high temperature and density by a histogram method

We study the QCD phase structure at high temperature and density adopting a histogram method. Because the quark determinant is complex at finite density, the Monte-Carlo method cannot be applied directly. We use a reweighting method and try to solve the problems which arise in the reweighting method, i.e. the sign problem and the overlap problem. We discuss the chemical potential dependence of the probability distribution function in the heavy quark mass region and examine the applicability of the approach in the light quark region.

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