Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: The Parent State of Quantum Phases

Abstract

The interplay between lattice gauge theories and fermionic matter accounts for fundamental physical phenomena ranging from the deconfinement of quarks in particle physics to quantum spin liquid with fractionalized anyons and emergent gauge structures in condensed matter physics. However, except for certain limits (for instance large number of flavors of matter fields), analytical methods can provide few concrete results. Here we show that the problem of compact U(1) lattice gauge theory coupled to fermionic matter in (2 + 1)D is possible to access via sign-problem-free quantum Monte Carlo simulations. One can hence map out the phase diagram as a function of fermion flavors and the strength of gauge fluctuations. By increasing the coupling constant of the gauge field, gauge confinement in the form of various spontaneous symmetry breaking phases such as valence bond solid (VBS) and Néel antiferromagnet emerge. Deconfined phases with algebraic spin and VBS correlation functions are also observed. Such deconfined phases are incarnation of an exotic states of matter, i.e. the algebraic spin liquid, which is generally viewed as the parent state of various quantum phases. The phase transitions between deconfined and confined phases, as well as that between the different confined phases provide various manifestations of deconfined quantum criticality. In particular, for four flavors, N f = 4, our data suggests a continuous quantum phase transition between the VBS and Néel order. We also provide preliminary theoretical analysis for these quantum phase transitions.

Dimensional crossover in the SU(4) Heisenberg model in the six-dimensional antisymmetric self-conjugate representation revealed by quantum Monte Carlo and linear flavor-wave theory

“…In particular, promoting N to a continuous variable, our results show that the SU(4) quantum antiferromagnet is close to a putative deconfined quantum critical point to the VBS. Various, yet to be numerically confirmed, field theories can be put forward to understand this quantum phase transition 25,45 in a two dimensional setting. Finally, the nature of the dimensional driven transition to the VBS remains to be studied.…”

Dynamics of compact quantum electrodynamics at large fermion flavor

“…Inspired by the numerical work of Ref. [1], there are recently several analytical works addressing the critical properties of them [42][43][44][45][46][47]. And the conclusions drawn there are that the U(1)-to-AFM and U(1)-to-VBS phase transitions are indeed possible and the higher-order perturbative RG calculations performed also suggest the possible range of critical exponents of these QED 3 -GN transitions within 1/N f and 4 − expansions [42][43][44][45][46][47].…”

“…Previous works have quickly established the understanding at the large fermion flavor (N f ) limit [9][10][11][12][13][14][15][16][17], as 1/N f expansion is controlled thence, but left the physically most interesting cases of small N f -for example N f = 2 corresponds to the spin-1/2 case of electrons -unsolved. The very recent breakthrough of quantum Monte Carlo (QMC) simulations of Z2 [23][24][25]27] and U(1) [1] gauge fields coupled to fermions provide the possibility of concrete investigations at the small N f , and the expected deconfinement-to-confinement phase transitions and special properties of these phases are discovered. In such settings, the interactions between fermions are mediated via the fluctuating gauge bosons, which resemble the situation of fractionalized particles and emergent gauge fields in several prototypical strongly correlated systems including, but not limited to, the low-energy description of the high-temperature superconductors [11,15,19], frustrated magnets [19,28,29] and deconfined quantum criticalities [30][31][32][33][34][35].…”

“…It is only till very recent, that in Ref. [1], with the help of fast updates and high level parallelization, that the phase diagram of U(1) gauge field coupled to fermion field at small N f has been mapped out, and the existence of U(1) deconfined phase, or algebraic quantum spin liquid in the condensed matter parlance [19], for N f = 2, 4, 6, 8 are discovered with certainty. However, even the latest QMC simulations are still by no means easy, suffering long autocorrelation time in the critical phase of U(1) deconfined spin liquid, the transitions from U(1) deconfined phase to various confined phases (antiferromagnetic insulator (AFM) phase for N f = 2, and valence bond solid (VBS) phase and AFM for N f = 4, 6, 8) have not been able to investigated in detail, both statically and dynamically.…”

Hierarchy of energy scales in an O(3) symmetric antiferromagnetic quantum critical metal: A Monte Carlo study

“…Among others, QCPs related to the breaking of antiferromagnetic Z 2 [39,40] and XY [17,37], ferromagnetic Z 2 [41][42][43], charge density wave [21], and nematic [19][20][21]44] order have been investigated. Other recent studies focused on deconfined QCPs where fermionic matter fields are coupled to Z 2 [45][46][47][48] and U (1) [49] lattice gauge theories.…”