A practical solution to the sign problem in a matrix model for dynamical compactification

Hartree–Fock–Bogolyubov calculations with Gaussian expansion method

The nuclear electric dipole moment is a very sensitive probe of CP violation beyond the standard model, and for light nuclei, it can be evaluated accurately using few-body calculational methods. In this talk, we present the deuteron, 3He, 3H, 6Li, and 9Be electric dipole moments calculated using the Gaussian expansion method with a realistic nuclear force, and assuming the one-meson exchange model for the P, CP-odd nuclear force. We then give future prospects for models beyond the standard model such as the supersymmetry.

Rotating systems in thermal equilibrium are ubiquitous in our world. In the context of high-energy physics, rotations would affect the phase structure of quantum chromodynamics (QCD). However, the standard Monte Carlo methods in rotating systems are problematic because the chemical potentials for the angular momenta (angular velocities) cause sign problems even for bosonic variables. In this article, we demonstrate that the complex Langevin method (CLM) may overcome this issue. We apply the CLM to the Yang–Mills (YM)-type one-dimensional matrix model (matrix quantum mechanics) that is a large-N reduction (or dimensional reduction) of the (D + 1)-dimensional U(N) pure YM theory [bosonic Banks–Fischler–Shenker–Susskind (BFSS) model]. This model shows a large-N phase transition at finite temperature, which is analogous to the confinement/deconfinement transition of the original YM theory, and our CLM predicts that the transition temperature decreases as the angular momentum chemical potential increases. In order to verify our results, we compute several quantities via the minimum sensitivity method and find good quantitative agreements. Hence, the CLM works properly in this rotating system. We also argue that our results are qualitatively consistent with a holography and the recent studies of the imaginary angular velocity in QCD. As a byproduct, we develop an analytic approximation to treat the so-called “small black hole” phase in the matrix model.

We perform a detailed comparison of results of the Gamow Shell Model (GSM) and the Gaussian Expansion Method (GEM) supplemented by the complex scaling (CS) method for the same translationally-invariant cluster-orbital shell model (COSM) Hamiltonian. As a benchmark test, we calculate the ground state $0^{+}$ and the first excited state $2^{+}$ of mirror nuclei $^{6}$He and $^{6}$Be in the model space consisting of two valence nucleons in $p$-shell outside of a $^{4}$He core. We find a good overall agreement of results obtained in these two different approaches, also for many-body resonances.

A bstract We systematically classify all supersymmetry-preserving mass deformations of SYM matrix models in all dimensions ( D = 3, 4, 6, 10). In D = 10, the polarized IKKT model emerges as the only possible deformation. In D = 4, we identify two massive models without a sign problem, making them attractive candidates for non-perturbative numerical studies.

Quantum Monte Carlo (QMC) methods are the gold standard for studying equilibrium properties of quantum many-body systems. However, in many interesting situations, QMC methods are faced with a sign problem, causing the severe limitation of an exponential increase in the runtime of the QMC algorithm. In this work, we develop a systematic, generally applicable, and practically feasible methodology for easing the sign problem by efficiently computable basis changes and use it to rigorously assess the sign problem. Our framework introduces measures of non-stoquasticity that-as we demonstrate analytically and numerically-at the same time provide a practically relevant and efficiently computable figure of merit for the severity of the sign problem. Complementing this pragmatic mindset, we prove that easing the sign problem in terms of those measures is generally an NP-complete task for nearest-neighbor Hamiltonians and simple basis choices by a reduction to the MAXCUT-problem.

We discuss the sign problem arising in Monte Carlo simulations of frustrated quantum spin systems. We show that for a class of ``semi-frustrated'' systems (Heisenberg models with ferromagnetic couplings $J_z(r) < 0$ along the $z$-axis and antiferromagnetic couplings $J_{xy}(r)=-J_z(r)$ in the $xy$-plane, for arbitrary distances $r$) the sign problem present for algorithms operating in the $z$-basis can be solved within a recent ``operator-loop'' formulation of the stochastic series expansion method (a cluster algorithm for sampling the diagonal matrix elements of the power series expansion of ${\rm exp}(-\beta H)$ to all orders). The solution relies on identification of operator-loops which change the configuration sign when updated (``merons'') and is similar to the meron-cluster algorithm recently proposed by Chandrasekharan and Wiese for solving the sign problem for a class of fermion models (Phys. Rev. Lett. {\bf 83}, 3116 (1999)). Some important expectation values, e.g., the internal energy, can be evaluated in the subspace with no merons, where the weight function is positive definite. Calculations of other expectation values require sampling of configurations with only a small number of merons (typically zero or two), with an accompanying sign problem which is not serious. We also discuss problems which arise in applying the meron concept to more general quantum spin models with frustrated interactions.

Inspired by the experimental discoveries of $T_{cc}$, $\Sigma_c(2800)$, and $\Lambda_c(2940)$ and the theoretical picture where they are $DD^*$, $DN$, and $D^*N$ molecular candidates, we investigate the double charm heptaquark system of $DD^*N$. We employ the one-boson-exchange model to deduce the pairwise $D$-$D^*$, $D$-$N$, and $D^*$-$N$ potentials and then study the $DD^*N$ system with the Gaussian expansion method. We find two good hadronic molecular candidates with $I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$ and $\frac{1}{2}(\frac{3}{2}^-)$ $DD^*N$ with only $s$-wave pairwise interactions. The conclusion remains unchanged even taking into account the $S$-$D$ mixing and coupled channel effects. In addition to providing the binding energies, we also calculate the root-mean-square radii of the $DD^*N$ system, which further support the molecular nature of the predicted states. They can be searched for at the upcoming LHC run 3 and run 4.

We systematically investigate the S-wave singly heavy tetraquark systems containing two or three strange quarks, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>Q</a:mi> <a:mi>s</a:mi> <a:mover accent="true"> <a:mi>s</a:mi> <a:mo stretchy="false">¯</a:mo> </a:mover> <a:mover accent="true"> <a:mi>s</a:mi> <a:mo stretchy="false">¯</a:mo> </a:mover> </a:math> , <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>Q</g:mi> <g:mi>n</g:mi> <g:mover accent="true"> <g:mi>s</g:mi> <g:mo stretchy="false">¯</g:mo> </g:mover> <g:mover accent="true"> <g:mi>s</g:mi> <g:mo stretchy="false">¯</g:mo> </g:mover> </g:math> , and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>Q</m:mi> <m:mi>s</m:mi> <m:mover accent="true"> <m:mi>s</m:mi> <m:mo stretchy="false">¯</m:mo> </m:mover> <m:mover accent="true"> <m:mi>n</m:mi> <m:mo stretchy="false">¯</m:mo> </m:mover> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>Q</m:mi> <m:mo>=</m:mo> <m:mi>c</m:mi> <m:mo>,</m:mo> <m:mi>b</m:mi> <m:mo>,</m:mo> <m:mi>n</m:mi> <m:mo>=</m:mo> <m:mi>u</m:mi> <m:mo>,</m:mo> <m:mi>d</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:math> , within the constituent quark potential model. We solve the four-body Schrödinger equation using the Gaussian expansion method and identify resonances via the complex scaling method. There are no bound states below the lowest two-meson thresholds. We obtain several compact resonances with <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msup> <u:mi>J</u:mi> <u:mi>P</u:mi> </u:msup> <u:mo>=</u:mo> <u:msup> <u:mn>0</u:mn> <u:mo>+</u:mo> </u:msup> <u:mo>,</u:mo> <u:msup> <u:mn>2</u:mn> <u:mo>+</u:mo> </u:msup> </u:math> in <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mi>Q</w:mi> <w:mi>s</w:mi> <w:mover accent="true"> <w:mi>s</w:mi> <w:mo stretchy="false">¯</w:mo> </w:mover> <w:mover accent="true"> <w:mi>s</w:mi> <w:mo stretchy="false">¯</w:mo> </w:mover> </w:math> , and <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:msup> <cb:mi>J</cb:mi> <cb:mi>P</cb:mi> </cb:msup> <cb:mo>=</cb:mo> <cb:msup> <cb:mn>2</cb:mn> <cb:mo>+</cb:mo> </cb:msup> </cb:math> in <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:mi>Q</eb:mi> <eb:mi>n</eb:mi> <eb:mover accent="true"> <eb:mi>s</eb:mi> <eb:mo stretchy="false">¯</eb:mo> </eb:mover> <eb:mover accent="true"> <eb:mi>s</eb:mi> <eb:mo stretchy="false">¯</eb:mo> </eb:mover> </eb:math> and <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"> <kb:mi>Q</kb:mi> <kb:mi>s</kb:mi> <kb:mover accent="true"> <kb:mi>s</kb:mi> <kb:mo stretchy="false">¯</kb:mo> </kb:mover> <kb:mover accent="true"> <kb:mi>n</kb:mi> <kb:mo stretchy="false">¯</kb:mo> </kb:mover> </kb:math> . The pole positions are mainly distributed around 7.0–7.2 GeV (bottom) and 3.7–3.9 GeV (charm), with widths from a few to several tens of MeV. These resonances decay into <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"> <qb:msub> <qb:mi>D</qb:mi> <qb:mi>s</qb:mi> </qb:msub> <qb:msup> <qb:mi>η</qb:mi> <qb:mo>′</qb:mo> </qb:msup> <qb:mo>,</qb:mo> <qb:msubsup> <qb:mi>D</qb:mi> <qb:mrow> <qb:mo stretchy="false">(</qb:mo> <qb:mi>s</qb:mi> <qb:mo stretchy="false">)</qb:mo> </qb:mrow> <qb:mo>*</qb:mo> </qb:msubsup> <qb:mi>ϕ</qb:mi> <qb:mo>,</qb:mo> <qb:msup> <qb:msub> <qb:mi>D</qb:mi> <qb:mi>s</qb:mi> </qb:msub> <qb:mo>*</qb:mo> </qb:msup> <qb:msup> <qb:mi>K</qb:mi> <qb:mo>*</qb:mo> </qb:msup> </qb:math> , and <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"> <ub:msubsup> <ub:mi>D</ub:mi> <ub:mi>s</ub:mi> <ub:mo>*</ub:mo> </ub:msubsup> <ub:msup> <ub:mover accent="true"> <ub:mi>K</ub:mi> <ub:mo stretchy="false">¯</ub:mo> </ub:mover> <ub:mo>*</ub:mo> </ub:msup> </ub:math> (and their bottom counterparts), providing targets for future experimental searches.

Reconstructed Gaussian basis to characterize flexural wave collimation in plates with periodic arrays of annular acoustic black holes

We investigate the tetraquark bound states that are manifestly exotic using three distinct few-body methods; Gaussian expansion method (GEM), resonating group method (RGM), and diffusion Monte Carlo (DMC). We refer to manifestly exotic states that do not involve a mixture with the conventional mesons through the creation and annihilation of $n\overline{n}$, where $n=u$, $d$. Our calculations are conducted with two types of quark models; the pure constituent quark model featuring one-gluon-exchange interactions and confinement interactions, and the chiral constituent quark model, supplemented by extra one-boson-exchange interactions. This study represents a comprehensive benchmark test of various few-body methods and quark models. Our findings reveal the superiority of GEM over RGM and DMC methods based on present implements for the tetraquark bound states. Additionally, we observe a tendency for the chiral quark model to overestimate the binding energies. We systematically explore the fully, triply, doubly, and singly heavy tetraquark states with ${J}^{P}={0}^{+},{1}^{+},{2}^{+}$, encompassing over 150 states in total. We successfully identify several bound states, including $[cc\overline{n}\overline{n}{]}_{{J}^{P}={1}^{+}}^{I=0}$, $[bb\overline{n}\overline{n}{]}_{{J}^{P}={1}^{+}}^{I=0}$, $[bc\overline{n}\overline{n}{]}_{{J}^{P}={0}^{+},{1}^{+},{2}^{+}}^{I=0}$, $[bs\overline{n}\overline{n}{]}_{{J}^{P}={0}^{+},{1}^{+}}^{I=0}$, $[cs\overline{n}\overline{n}{]}_{{J}^{P}={0}^{+}}^{I=0}$, and $[bb\overline{n}\overline{s}{]}_{{J}^{P}={1}^{+}}$, all found to be bound states below the dimeson thresholds.

We formulate a computational method to evaluate the overlap integral of the shell-model and cluster-model wave functions. The framework is applied to the system of the core plus two neutrons, and the magnitude of the overlap of the shell-model configuration (core + $n$ + $n$) and the di-neutron cluster one (core + $2n$) is explored. We have found that the magnitude of the overlap integral is prominently enhanced when two neutrons occupy shell-model orbits with low orbital angular momenta, such as $s$- and $p$-wave orbits. The shell–cluster overlap is calculated in systems with $jj$-closed cores plus two neutrons, and the enhancement due to occupation of the $s$ or $p$ orbit also occurs in the systematic calculation. The effect of the configuration interaction on the shell–cluster overlap integrals is also discussed.

In the framework of chiral quark model, the mass spectrum of $\eta_c(ns) (n=1,...,6)$ is studied with Gaussian expansion method. With the wave functions obtained in the study of mass spectrum, the open flavor two-body strong decay widths are calculated by using $^3P_0$ model. The results show that the masses of $\eta_c(1S)$ and $\eta_c(2S)$ are consistent with the experimental data. The explanation of X(3940) as $\eta_c(3S)$ is disfavored for X(3940) is a narrow state, $\Gamma=37^{+26}_{-15} \pm 8 $ MeV, while the open flavor two-body strong decay width of $\eta_c(3S)$ is about 200 MeV in our calculation. Although the mass of X(4160) is about 100 MeV less than that of $\eta_c(4S)$, the assignment of X(4160) as $\eta_c(4S)$ can not be excluded because the open flavor two-body strong decay width of $\eta_c(4S)$ is consistent with the experimental value of X(4160) and the branching ratios of $\eta_c(4S)$ are compatible with that of X(4160), and the mass of $\eta_c(4S)$ can be shifted downwards by taking into account the coupling effect of the open charm channels. There are still no good candidates to $\eta_c(5S)$ and $\eta_c(6S)$.

In the framework of color flux-tube model with a four-body confinement potential, the lowest charged tetraquark states $[Qq][\bar{Q}'\bar{q}']~(Q=c,b,q=u,d,s)$ are studied by using the variational method, Gaussian expansion method. The results indicate that some compact resonance states can be formed, the states can not decay into two color singlet mesons $Q\bar{q}'$ and $\bar{Q}'q$ through the breakdown and recombination of color flux tubes but into $Q\bar{Q}'$ and $q\bar{q}'$. The four-body confinement potential is an crucial dynamical mechanism for the formation of states, The decay mechanism is similar to that of compound nucleus and therefore the states should be called "color confined, multi-quark resonance" states. The newly observed charged states $Z_c(3900)$ and $Z_c(4025)/Z_c(4020)$ can be accommodated in the color flux-tube model and can be interpreted as the $S$-wave tetraquark states $[cu][{\bar{c}\bar{d}}]$ with quantum numbers $I=1$ and $J=1$ and 2, respectively.

Stimulated by the newly observed charged hidden-charm state ${Z}_{cs}(3985{)}^{\ensuremath{-}}$ by BESIII Collaboration, ${Z}_{cs}(4000{)}^{+}$, ${Z}_{cs}(4220{)}^{+}$ and the excited ${B}_{s}^{0}$ states by LHCb Collaboration, a full calculation including masses, decay widths, and the inner structures of the states has emerged in the chiral quark model. For ${Z}_{cs}$ states, we assign quantum numbers $I({J}^{P})=\frac{1}{2}({1}^{+})$ and quark composition $c\overline{c}s\overline{u}$ according to the experiment. For ${B}_{s}^{0}$ states, systematically, investigations are performed with $I({J}^{P})=0({0}^{+}),0({1}^{+}),0({2}^{+})$ in both two-body $b\overline{s}$ and four-body $b\overline{s}q\overline{q}$ ($q=u$ or $d$) systems. Each tetraquark calculation takes all structures including meson-meson, diquark-antidiquark, and all possible color configurations into account. Among the numerical techniques to solve the two-body and four-body Schr\"odinger equation, the spatial wave functions are expanded in series of Gaussian basis functions for high precision, which is the way Gaussian expansion method (GEM) so called. Our results indicate that the low-lying states of the four-quark system are all higher than the corresponding thresholds either for $c\overline{c}s\overline{u}$ or for $b\overline{s}q\overline{q}$ systems. With the help of the real scaling method, we found two molecular resonance states with masses of 4023 and 4042 MeV for the $c\overline{c}s\overline{u}$ system. The state $c\overline{c}s\overline{u}(4042)$ has a close mass and decay width with the recent observed state ${Z}_{cs}(3985{)}^{\ensuremath{-}}$. For the $b\overline{s}q\overline{q}$ system with $J=0$, some resonance states are also found. The newly observed excited ${B}_{s}^{0}$ states can be accommodated in the chiral quark model as $2S$ or $1D$ states, and the mixing with four-quark states also needs to be considered.