Using matrix product states, we explore numerically the phenomenology of string breaking in a non-Abelian lattice gauge theory, namely 1+1 dimensional SU(2). The technique allows us to study the static potential between external heavy charges, as traditionally explored by Monte Carlo simulations, but also to simulate the real-time dynamics of both static and dynamical fermions, as the latter are fully included in the formalism. We propose a number of observables that are sensitive to the presence or breaking of the flux string, and use them to detect and characterize the phenomenon in each of these setups.
Calculations of the chiral condensate on the lattice using staggered fermions and the Lanczos algorithm are presented. Four gauge fields are considered: the quenched non-Abelian field, an Abelian projected field, and monopole and photon fields further decomposed from the Abelian field. Abelian projection is performed in maximal Abelian gauge and in Polyakov gauge. The results show that monopoles in maximal Abelian gauge largely reproduce the chiral condensate values of the full non-Abelian theory, in both SU(2) and SU(3) color.
Chiral symmetry breaking parameters are calculated in quenched SU(2) gauge theory and with Abelian gauge fields projected in maximal Abelian gauge and in field strength gauge. Maximal Abelian gauge projected fields lead to chiral condensate values which are quite similar to those of the full nonabelian theory. Pseudoscalar and vector meson correlators are calculated and found to be reproduced by the use of maximal Abelian gauge fields for small quark masses. In field-strength gauge, Abelian-projected fields give a chiral condensate which closely resembles the results of strongly coupled ($β<1$…
Calculations of the chiral condensate $\langle \barψ ψ\rangle$ on the lattice using staggered fermions and the Lanczos algorithm are presented. Three gauge fields are considered: the quenched non-Abelian field, the Abelian field projected in the maximal Abelian gauge, and the monopole field further decomposed from the Abelian field. The results show that the Abelian monopoles largely reproduce the chiral condensate values of the full non-Abelian theory, both in SU(2) and in SU(3).
Quantum Simulations of Two-Dimensional Non-Abelian Adjoint String Breaking
Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；IBM Quantum, IBM Research（IBM量子，IBM研究院）；National Energy Research Scientific Computing Center（国家能源研究科学计算中心）
In the Abelian projection the Yang--Mills theory contains Abelian gauge fields (diagonal degrees of freedom) and the Abelian matter fields (off-diagonal degrees) described by a complicated action. The matter fields are essential for the breaking of the adjoint string. We obtain numerically the effective action of the Abelian gauge and the Abelian matter fields in quenched SU(2) QCD and show that the Abelian matter fields provide an essential contribution to the total action even in the infrared region. We also observe the breaking of an Abelian analog of the adjoint string using Abelian operat…
We study the breaking of the string spanned between test charges in the three dimensional Abelian Higgs model with compact gauge field and fundamentally charged Higgs field at zero temperature. In agreement with current expectations we demonstrate that string breaking is associated with pairing of monopoles. However, the string breaking is not accompanied by an ordinary phase transition.
We present clear numerical evidence for string breaking in three-dimensional SU(2) gauge theory with fundamental bosonic matter through a mixing analysis between Wilson loops and meson operators representing bound states of a static source and a dynamical scalar. The breaking scale is calculated in the continuum limit. In units of the lightest glueball we find $r_{\rm b} m_G\approx13.6$. The implications of our results for QCD are discussed.
Real-Time String Dynamics in a $2+1$D Non-Abelian Lattice Gauge Theory: String Breaking, Glueball Formation, Baryon Blockade, and Tension Reduction
Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Dipartimento di Fisica, Università di Torino（都灵大学物理系）；Ludwig Maximilian University of Munich（慕尼黑大学）；Arnold Sommerfeld Center for Theoretical Physics (ASC)（阿诺德·索末菲理论物理中心）；College of Science, Kyung Hee University（庆熙大学理学院）
We investigate the effect of a uniform background magnetic field on the chiral symmetry breaking in SU(2) Yang-Mills theory on the lattice. We observe that the chiral condensate grows linearly with the field strength B up to \sqrt{e B} = 3 GeV as predicted by chiral perturbation theory for full QCD. As the temperature increases the coefficient in front of the linear term gets smaller. In the magnetic field near-zero eigenmodes of the Dirac operator tend to have more regular structure with larger (compared to zero-field case) Hausdorff dimensionality. We suggest that the delocalization of near-…
We analyze the vacuum structure of SU(2) QCD with multiple massless adjoint representation fermions formulated on a small spatial $S^1 \times \R^3$. The absence of thermal fluctuations, and the fact that quantum fluctuations favoring the vacuum with unbroken center symmetry in a weakly coupled regime renders the interesting dynamics of these theories analytically calculable. Confinement, the area law behavior for large Wilson loops, and the generation of the mass gap in the gluonic sector are shown analytically. By abelian duality transformation, the long distance effective theory of QCD is ma…
We study the Landau gauge photon propagator in the three--dimensional Abelian Higgs model with compact gauge field and fundamentally charged matter in the London limit. The total gauge field is split into singular and regular parts. On the confinement side of the string breaking crossover the momentum dependence of the total propagator is characterized by an anomalous dimension similarly to 3D compact QED. At the crossover and throughout the Higgs region the anomalous dimension disappears. This result perfectly agrees with recent observations that the monopole--antimonopole plasma leads to non…
Far-from-equilibrium dynamics of SU(2) gauge theory with Wilson fermions is studied in 1+1 space-time dimensions using a real-time lattice approach. Lattice improved Hamiltonians are shown to be very efficient in simulating Schwinger pair creation and emergent phenomena such as plasma oscillations. As a consequence, significantly smaller lattices can be employed to approach continuum physics in the infinite-volume limit as compared to unimproved implementations. This allows us to compute also higher-order correlation functions including four fermion fields, which give unprecedented insights in…
The center-stabilized multiflavor QCD* theories formulated on R_3 x S_1 exhibit both Abelian and non-Abelian confinement as a function of the S_1 radius, similar to the Seiberg-Witten theory as a function of the mass deformation parameter. For sufficiently small number of flavors and small r(S_1), we show occurence of a mass gap in gauge fluctuations, and linear confinement. This is a regime of confinement without continuous chiral symmetry breaking (χSB). Unlike one-flavor theories where there is no phase transition in r(S_1), the multiflavor theories possess a single phase transition associa…
The order parameters which are thought to detect U(1) gauge symmetry breaking in a superconductor are both non-local and gauge dependent. For that reason they are also ambiguous as a guide to phase structure. We point out that a global subgroup of the local U(1) gauge symmetry may be regarded, in analogy to non-abelian theories, as a "custodial" symmetry affecting the matter field alone, and construct, along the lines of our previous work, a new gauge-invariant criterion for breaking symmetries of this kind. It is shown that spontaneous breaking of custodial symmetry is a necessary condition f…
We study the properties of topological defects in the lattice compact Abelian Higgs Model with charge Q=2 matter field. We find that monopoles and antimonopoles form chain-like structures which are dense in the confinement/symmetric phase. In this phase the mentioned structures explain both the confinement of single-charged and the breaking of strings spanned between doubly-charged test particles. This observation helps to understand how the non-diagonal gluons, once taken into consideration in the Abelian projection of gluodynamics, could reproduce in this framework the string breaking for ad…
The string breaking is discussed in U(1)^{N-1} Abelian effective theories of QCD. When a screening is expected, the static potential shows a flattening in the long-range region and a linear behavior in the intermediate region. We show why the screening is better observed in the Polyakov-loop correlators than in the Wilson loops. The breaking of the adjoint string is explained without the Z(N) picture.
Much about the confinement and dynamical symmetry breaking in QCD might be learned from models with supersymmetry. In particular, models based on N=2 supersymmetric theories with gauge groups SU(N), SO(N) and $USp(2 N)$ and with various number of flavors, give deep dynamical hints about these phenomena. For instance, the BPS non-abelian monopoles can become the dominant degrees of freedom in the infrared due to quantum effects. Upon condensation (which can be triggered in these class of models by perturbing them with an adjoint scalar mass) they induce confinement with calculable pattern of dy…
Starting from the bosonic part of N=2 Super QCD with a 'Seiberg-Witten' N=2 breaking mass term, we obtain string BPS conditions for arbitrary semi-simple gauge groups. We show that the vacuum structure is compatible with a symmetry breaking scheme which allows the existence of Z_k-strings and which has Spin(10) -> SU(5) x Z_2 as a particular case. We obtain BPS Z_k-string solutions and show that they satisfy the same first order differential equations as the BPS string for the U(1) case. We also show that the string tension is constant, which may cause a confining potential between monopoles i…
Recently (hep-th/0104171) we considered N=2 super Yang-Mills with a N=2 mass breakingn term and showed the existence of BPS Z_{k}-string solutions for arbitrary simple gauge groups which are spontaneously broken to non-Abelian residual gauge groups. We also calculated their string tensions exactly. In doing so, we have considered in particular the hypermultiplet in the same representation as the one of a diquark condensate. In the present work we analyze some of the different phases of the theory and find that the magnetic fluxes of the monopoles are multiple of the fundamental Z_{k}-string fl…
