arXiv subjects

Anyi Li

Publications and source records attributed to Anyi Li.

32 records · Page 2Linked to original sources

arXiv2012

Fermion bag solutions to some sign problems in four-fermion field theories

Lattice four-fermion models containing $N$ flavors of staggered fermions, that are invariant under $Z_2$ and U(1) chiral symmetries, are known to suffer from sign problems when formulated using the auxiliary field approach. Although these problems have been ignored in previous studies, they can be severe. Here we show that the sign problems disappear when the models are formulated in the fermion bag approach, allowing us to solve them rigorously for the first time.

hep-lat↗

arXiv2012

Fermion bags, duality and the three dimensional massless lattice Thirring model

The recently proposed fermion bag approach is a powerful technique to solve some four-fermion lattice field theories. Due to the existence of a duality between strong and weak couplings, the approach leads to efficient Monte Carlo algorithms in both these limits. The new method allows us for the first time to accurately compute quantities close to the quantum critical point in the three dimensional lattice Thirring model with massless fermions on large lattices. The critical exponents at the quantum critical point are found to be $ν=0.85(1)$, $η= 0.65(1)$ and $η_ψ= 0.37(1)$.

hep-lat↗

arXiv2011

Critical point of $N_f = 3$ QCD from lattice simulations in the canonical ensemble

A canonical ensemble algorithm is employed to study the phase diagram of $N_f = 3$ QCD using lattice simulations. We lock in the desired quark number sector using an exact Fourier transform of the fermion determinant. We scan the phase space below $T_c$ and look for an S-shape structure in the chemical potential, which signals the coexistence phase of a first order phase transition in finite volume. Applying Maxwell construction, we determine the boundaries of the coexistence phase at three temperatures and extrapolate them to locate the critical point. Using an improved gauge action and improved Wilson fermions on lattices with a spatial extent of $1.8 \fm$ and quark masses close to that of the strange, we find the critical point at $T_E = 0.925(5) T_c$ and baryon chemical potential $μ_B^E = 2.60(8) T_c$.

hep-ph↗

arXiv2011

The generalized fermion-bag approach

We present a new approach to some four-fermion lattice field theories which we call the generalized fermion bag approach. The basic idea is to identify unpaired fermionic degrees of freedom that cause sign problems and collect them in a bag. Paired fermions usually act like bosons and do not lead to sign problems. A resummation of all unpaired fermion degrees of freedom inside the bag is sufficient to solve the fermion sign problem in a variety of interesting cases. Using a concept of duality we then argue that the size of the fermion bags is small both at strong and weak couplings. This allows us to construct efficient algorithms in both these limits. Using the fermion bag approach, we study the quantum phase transition of the 3D massless lattice Thirrring model which is of interest in the context of Graphene. Using our method we are able to solve the model on lattices as large as $40^3$ with moderate computational resources. We obtain the precise location of the quantum critical point and the values of the critical exponents through this study.

hep-lat↗

arXiv2010

Anomaly and a QCD-like phase diagram with massive bosonic baryons

We study a strongly coupled $Z_2$ lattice gauge theory with two flavors of quarks, invariant under an exact $\mathrm{SU}(2)\times \mathrm{SU}(2) \times \mathrm{U}_A(1) \times \mathrm{U}_B(1)$ symmetry which is the same as QCD with two flavors of quarks without an anomaly. The model also contains a coupling that can be used to break the $\mathrm{U}_A(1)$ symmetry and thus mimic the QCD anomaly. At low temperatures $T$ and small baryon chemical potential $μ_B$ the model contains massless pions and massive bosonic baryons similar to QCD with an even number of colors. In this work we study the $T-μ_B$ phase diagram of the model and show that it contains three phases : (1) A chirally broken phase at low $T$ and $μ_B$, (2) a chirally symmetric baryon superfluid phase at low $T$ and high $μ_B$, and (3) a symmetric phase at high $T$. We find that the nature of the finite temperature chiral phase transition and in particular the location of the tricritical point that seperates the first order line from the second order line is affected significantly by the anomaly.

hep-lat↗

arXiv2010

Finite density phase transition of QCD with $N_f=4$ and $N_f=2$ using canonical ensemble method

In a progress toward searching for the QCD critical point, we study the finite density phase transition of $N_f = 4$ and 2 lattice QCD at finite temperature with the canonical ensemble approach. We develop a winding number expansion method to accurately project out the particle number from the fermion determinant which greatly extends the applicable range of baryon number sectors to make the study feasible. Our lattice simulation was carried out with the clover fermions and improved gauge action. For a given temperature, we calculate the baryon chemical potential from the canonical approach to look for the mixed phase as a signal for the first order phase transition. In the case of $N_f=4$, we observe an "S-shape" structure in the chemical potential-density plane due to the surface tension of the mixed phase in a finite volume which is a signal for the first order phase transition. We use the Maxwell construction to determine the phase boundaries for three temperatures below $T_c$. The intersecting point of the two extrapolated boundaries turns out to be at the expected first order transition point at $T_c$ with $μ= 0$. This serves as a check for our method of identifying the critical point. We also studied the $N_f =2$ case, but do not see a signal of the mixed phase for temperature as low as 0.83 $T_c$.

hep-lat↗

arXiv2010

Fermion bag approach to the sign problem in strongly coupled lattice QED with Wilson fermions

We explore the sign problem in strongly coupled lattice QED with one flavor of Wilson fermions in four dimensions using the fermion bag formulation. We construct rules to compute the weight of a fermion bag and show that even though the fermions are confined into bosons, fermion bags with negative weights do exist. By classifying fermion bags as either simple or complex, we find numerical evidence that complex bags with positive and negative weights come with almost equal probabilities and this leads to a severe sign problem. On the other hand simple bags mostly have a positive weight. Since the complex bags almost cancel each other, we suggest that eliminating them from the partition function may be a good approximation. This modified partition function suffers only from a mild sign problem. We also find a simpler model which does not suffer from any sign problem and may still be a good approximation at small and intermediate values of the hopping parameter. We also prove that when the hopping parameter is strictly infinite all fermion bags are non-negative.

hep-lat↗

arXiv2010

Study of QCD critical point using the canonical ensemble method

The existence of the QCD critical point at non-zero baryon density is not only of great interest for experimental physics but also a challenge for the theory. Any hint of the existence of the first order phase transition and, particularly, its critical point will be valuable towards a full understanding of the QCD phase diagram. We use lattice simulation based on the canonical ensemble method to explore the finite baryon density and finite temperature region and look for the QCD critical point. As a benchmark, we run simulations for the four degenerate flavor QCD where we observe a clear signal of the expected first order phase transition. In the two flavor case, we do not see any signal for temperatures as low as $0.83 \rm{T_c}$. Although our real world contains two light quarks and one heavier quark, three degenerate flavor case shares a lot of similar phase structures as the QCD. We scan the phase diagram using clover fermions with $m_π\approx 700{MeV}$ on $6^3\times4$ lattices. The baryon chemical potential is measured as we increase the baryon number and we see the characteristic "S-shape" that signals the first order phase transition. We determine the phase boundaries by Maxwell construction and report our preliminary results for the location of critical point for the present lattice.

hep-lat↗

arXiv2009

Study of QCD critical point using canonical ensemble method

The existence of the QCD critical point at non-zero baryon density is not only of great interest for experimental physics but also a challenge for the theory. We use lattice simulations based on the canonical ensemble method to explore the finite baryon density region and look for the critical point. We scan the phase diagram of QCD with three degenerate quark flavors using clover fermions with $m_π\approx 700{MeV}$ on $6^3\times4$ lattices. We measure the baryon chemical potential as we increase the density and we see the characteristic "S-shape" that signals the first order phase transition. We determine the phase boundary by Maxwell construction and report our preliminary results for the location of critical point.

hep-lat↗

arXiv2008

Winding number expansion for the canonical approach to finite density simulations

The canonical partition function approach was designed to avoid the overlap problem that affects the lattice simulations of nuclear matter at high density. The method employs the projections of the quark determinant on a fix quark number sector. When the quark number is large, the evaluation of the projected determinant becomes numerically unstable. In this paper a different evaluation method based on expanding the determinant in terms of loops winding around the lattice is studied. We show that this method is stable and significantly faster than our original algorithm. This greatly expands the range of quark numbers that we can simulate effectively.

hep-lat↗

arXiv2008

Finite Density Simulations with Canonical Ensemble

QCD at non-zero baryon density is expected to have a critical point where the zero-density cross-over turns into a first order phase transition. To identify this point we scan the density-temperature space using a canonical ensemble method. For a given temperature, we plot the chemical potential as a function of density looking for an "S-shape" as a signal for a first order transition. We carried out simulations using Wilson fermions with $m_π\approx 1{GeV}$ on $6^3\times 4$ lattices. As a benchmark, we ran four flavors simulations where we observe a clear signal. In the two flavors case we do not see any signal for temperatures as low as $0.83 T_c$. Preliminary results for the three flavor case are also presented.

hep-lat↗

arXiv2007

Finite density simulations using a determinant estimator

Previous investigations have shown that the canonical approach to simulating QCD at finite density is promising. The algorithm we used in our earlier work employs an exact calculation of the fermionic determinant which limits the size of the lattices we can simulate. Interesting questions can only be answered if we simulate at larger volume. In this paper we explore an algorithm, Hybrid Noisy Monte Carlo, that employs a determinant estimator rather than an exact calculation. We first present the technical aspects of the estimator, check that the algorithm is correct by comparing it with our previous study, and then discuss its merits. We will also discuss the challenges faced when simulating larger lattice volumes.

hep-lat↗

arXiv2007

New results using the canonical approach to finite density QCD

We present some new results regarding simulations of finite density QCD based on a canonical approach. A previous study has shown that such simulations are feasible, at least on small lattices. In the current study, we investigate some of the issues left open: we study the errors introduced by our approximation of the action and we show how to tune it to reduce the cost of the simulations while keeping the errors under control. To further reduce the cost of the simulations, we check the reliability of reweighting method with respect to the baryon number. Finally, using these optimizations, we carry out the simulations at larger densities than in our previous study to look for signals of a phase transition.

hep-lat↗

arXiv2006

Reweighting method in finite density lattice QCD

Finite density simulations require dynamical fermions which are computationally demanding. We employ Ferrenberg and Swendsen reweighting method to reduce the number of ensembles needed. We use their method to do a combined reweighting in both $β$ and quark number $k$ on an ensemble generated by the Kentucky group.

hep-lat↗