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F. -J. Jiang

Publications and source records attributed to F. -J. Jiang.

At least 37 records · Page 2Linked to original sources
arXiv2014

Real-Time Simulation of Large Open Quantum Spin Systems driven by Measurements

We consider a large quantum system with spins $\frac{1}{2}$ whose dynamics is driven entirely by measurements of the total spin of spin pairs. This gives rise to a dissipative coupling to the environment. When one averages over the measurement results, the corresponding real-time path integral does not suffer from a sign problem. Using an efficient cluster algorithm, we study the real-time evolution of a 2-d Heisenberg antiferromagnet, which is driven to a disordered phase, either by sporadic measurements or by continuous monitoring described by Lindblad evolution.

cond-mat.str-el↗
arXiv2013

Crystalline Confinement

We show that exotic phases arise in generalized lattice gauge theories known as quantum link models in which classical gauge fields are replaced by quantum operators. While these quantum models with discrete variables have a finite-dimensional Hilbert space per link, the continuous gauge symmetry is still exact. An efficient cluster algorithm is used to study these exotic phases. The $(2+1)$-d system is confining at zero temperature with a spontaneously broken translation symmetry. A crystalline phase exhibits confinement via multi-stranded strings between charge-anti-charge pairs. A phase transition between two distinct confined phases is weakly first order and has an emergent spontaneously broken approximate $SO(2)$ global symmetry. The low-energy physics is described by a $(2+1)$-d $\mathbb{R}P(1)$ effective field theory, perturbed by a dangerously irrelevant $SO(2)$ breaking operator, which prevents the interpretation of the emergent pseudo-Goldstone boson as a dual photon. This model is an ideal candidate to be implemented in quantum simulators to study phenomena that are not accessible using Monte Carlo simulations such as the real-time evolution of the confining string and the real-time dynamics of the pseudo-Goldstone boson.

hep-lat↗
arXiv2013

Monte Carlo determination of the critical exponents for a quantum phase transition of a dimerized spin-1/2 Heisenberg model

We simulate the spin-1/2 Heisenberg model with a spatially staggered anisotropy using first principles Monte Carlo method. In particular, the critical exponents $β/ν$ and $ω$ associated with the quantum phase transition induced by dimerization are determined with high precision. Here $β$ and $ν$ are the exponents related to the magnetization and the correlation length, respectively. In addition, $ω$ is the confluent exponent. With very accurate data of the relevant observables, we first obtain a value of $ω$ compatible with the known result in the O(3) universality class. Further, using either the value of $ω$ determined here or the established one in the literature, the exponent $β/ν$ calculated from our data is in quantitative agreement with the known result $β/ν= 0.519(1)$ as well. Our investigation suggests that the quantum phase transition studied here is fully consistent with the O(3) universality class.

cond-mat.str-el↗
arXiv2013

Investigation of a universal behavior between Néel temperature and staggered magnetization density for a three-dimensional quantum antiferromagnet

We simulate the three-dimensional quantum Heisenberg model with a spatially anisotropic ladder pattern using the first principles Monte Carlo method. Our motivation is to investigate quantitatively the newly established universal relation $T_N/\sqrt{c^3}$ $\propto$ ${\cal M}_s$ near the quantum critical point (QCP) associated with dimerization. Here $T_N$, $c$, and ${\cal M}_s$ are the Néel temperature, the spinwave velocity, and the staggered magnetization density, respectively. For all the physical quantities considered here, such as $T_N$ and ${\cal M}_s$, our Monte Carlo results agree nicely with the corresponding results determined by the series expansion method. In addition, we find it is likely that the effect of a logarithmic correction, which should be present in (3+1)-dimensions, to the relation $T_N/\sqrt{c^3}$ $\propto$ ${\cal M}_s$ near the investigated QCP only sets in significantly in the region with strong spatial anisotropy.

cond-mat.str-el↗
arXiv2013

The (2+1)-d U(1) Quantum Link Model Masquerading as Deconfined Criticality

The $(2+1)$-d U(1) quantum link model is a gauge theory, amenable to quantum simulation, with a spontaneously broken SO(2) symmetry emerging at a quantum phase transition. Its low-energy physics is described by a $(2+1)$-d $\RP(1)$ effective field theory, perturbed by a dangerously irrelevant SO(2) breaking operator, which prevents the interpretation of the emergent pseudo-Goldstone boson as a dual photon. At the quantum phase transition, the model mimics some features of deconfined quantum criticality, but remains linearly confining. Deconfinement only sets in at high temperature.

cond-mat.str-el↗
arXiv2012

Quantum phase transitions of 2-d dimerized spin-1/2 Heisenberg models with spatial anisotropy

Motivated by the unexpected Monte Carlo results as well as the theoretical proposal of a large correction to scaling for the critical theory of the 2-d staggered-dimer spin-1/2 Heisenberg model on the square lattice, we study the phase transitions induced by dimerization of several dimerized quantum Heisenberg models with spatial anisotropy using first principles Monte Carlo method. Remarkably, while our Monte Carlo data for all the models considered here, including the herringbone- and ladder-dimer models on the square lattice, are compatible with the recently proposed scenario of an enhanced correction to scaling, we find it is likely that the enhanced correction to scaling manifests itself as amplification of the nonuniversal prefactors appeared in the scaling forms. In other words, our data are in consistence with the established numerical values for the critical exponents, including the confluent exponent, in the O(3) universality class. Convincing numerical evidence is provided to support this proposed scenario.

cond-mat.str-el↗
arXiv2012

Symmetry Analysis of Holes Localized on a Skyrmion in a Doped Antiferromagnet

We use the low-energy effective field theory for holes coupled to the staggered magnetization in order to investigate the localization of holes on a Skyrmion in a square lattice antiferromagnet. When two holes get localized on the same Skyrmion, they form a bound state. The quantum numbers of the bound state are determined by the quantization of the collective modes of the Skyrmion. Remarkably, for p-wave states the quantum numbers are the same as those of a hole-pair bound by one-magnon exchange. Two holes localized on a Skyrmion with winding number $n = 1$ or 2 may have s- or d-wave symmetry as well. Possible relations with preformed Cooper pairs of high-temperature superconductors are discussed.

cond-mat.str-el↗
arXiv2011

Systematic Low-Energy Effective Field Theory for Magnons and Holes in an Antiferromagnet on the Honeycomb Lattice

Based on a symmetry analysis of the microscopic Hubbard and t-J models, a systematic low-energy effective field theory is constructed for hole-doped antiferromagnets on the honeycomb lattice. In the antiferromagnetic phase, doped holes are massive due to the spontaneous breakdown of the $SU(2)_s$ symmetry, just as nucleons in QCD pick up their mass from spontaneous chiral symmetry breaking. In the broken phase the effective action contains a single-derivative term, similar to the Shraiman-Siggia term in the square lattice case. Interestingly, an accidental continuous spatial rotation symmetry arises at leading order. As an application of the effective field theory we consider one-magnon exchange between two holes and the formation of two-hole bound states. As an unambiguous prediction of the effective theory, the wave function for the ground state of two holes bound by magnon exchange exhibits $f$-wave symmetry.

cond-mat.str-el↗
arXiv2011

Solving the puzzle of an unconventional phase transition for a 2d dimerized quantum Heisenberg model

Motivated by the indication of a new critical theory for the spin-1/2 Heisenberg model with a spatially staggered anisotropy on the square lattice as suggested in \cite{Wenzel08}, we re-investigate the phase transition of this model induced by dimerization using first principle Monte Carlo simulations. We focus on studying the finite-size scaling of $ρ_{s1} 2L$ and $ρ_{s2} 2L$, where $L$ stands for the spatial box size used in the simulations and $ρ_{si}$ with $i \in \{1,2\}$ is the spin-stiffness in the $i$-direction. Remarkably, while we do observe a large correction to scaling for the observable $ρ_{s1}2L$ as proposed in \cite{Fritz11}, the data for $ρ_{s2}2L$ exhibit a good scaling behavior without any indication of a large correction. As a consequence, we are able to obtain a numerical value for the critical exponent $ν$ which is consistent with the known O(3) result with moderate computational effort. Specifically, the numerical value of $ν$ we determine by fitting the data points of $ρ_{s2}2L$ to their expected scaling form is given by $ν=0.7120(16)$, which agrees quantitatively with the most accurate known Monte Carlo O(3) result $ν= 0.7112(5)$. Finally, while we can also obtain a result of $ν$ from the observable second Binder ratio $Q_2$ which is consistent with $ν=0.7112(5)$, the uncertainty of $ν$ calculated from $Q_2$ is more than twice as large as that of $ν$ determined from $ρ_{s2}2L$.

cond-mat.str-el↗
arXiv2011

Constraint Effective Potential of the Magnetization in the Quantum XY Model

Using an improved estimator in the loop-cluster algorithm, we investigate the constraint effective potential of the magnetization in the spin $\tfrac{1}{2}$ quantum XY model. The numerical results are in excellent agreement with the predictions of the corresponding low-energy effective field theory. After its low-energy parameters have been determined with better than permille precision, the effective theory makes accurate predictions for the constraint effective potential which are in excellent agreement with the Monte Carlo data. This shows that the effective theory indeed describes the physics in the low-energy regime quantitatively correctly.

cond-mat.str-el↗
arXiv2011

Subtlety of Studying the Critical Theory of a Second Order Phase Transition

We study the quantum phase transition from a super solid phase to a solid phase of rho = 1/2 for the extended Bose-Hubbard model on the honeycomb lattice using first principles Monte Carlo calculations. The motivation of our study is to quantitatively understand the impact of theoretical input, in particular the dynamical critical exponent z, in calculating the critical exponent nu. Hence we have carried out four sets of simulations with beta = 2N^{1/2}, beta = 8N^{1/2}, beta = N/2, and beta = N/4, respectively. Here beta is the inverse temperature and N is the numbers of lattice sites used in the simulations. By applying data collapse to the observable superfluid density rho_{s2} in the second spatial direction, we confirm that the transition is indeed governed by the superfluid-insulator universality class. However we find it is subtle to determine the precise location of the critical point. For example, while the critical chemical potential (mu/V)_c occurs at (mu/V)_c = 2.3239(3) for the data obtained using beta = 2N^{1/2}, the (mu/V)_c determined from the data simulated with beta = N/2 is found to be (mu/V)_c = 2.3186(2). Further, while a good data collapse for rho_{s2}N can be obtained with the data determined using beta = N/4 in the simulations, a reasonable quality of data collapse for the same observable calculated from another set of simulations with beta = 8N^{1/2} can hardly be reached. Surprisingly, assuming z for this phase transition is determined to be 2 first in a Monte Carlo calculation, then a high quality data collapse for rho_{s2}N can be achieved for (mu/V)_c ~ 2.3184 and nu ~ 0.7 using the data obtained with beta = 8N^{1/2}. Our results imply that one might need to reconsider the established phase diagrams of some models if the accurate location of the critical point is crucial in obtaining a conclusion.

cond-mat.stat-mech↗
arXiv2010

Very High Precision Determination of Low-Energy Parameters: The 2-d Heisenberg Quantum Antiferromagnet as a Test Case

The 2-d spin 1/2 Heisenberg antiferromagnet with exchange coupling $J$ is investigated on a periodic square lattice of spacing $a$ at very small temperatures using the loop-cluster algorithm. Monte Carlo data for the staggered and uniform susceptibilities are compared with analytic results obtained in the systematic low-energy effective field theory for the staggered magnetization order parameter. The low-energy parameters of the effective theory, i.e.\ the staggered magnetization density ${\cal M}_s = 0.30743(1)/a^2$, the spin stiffness $ρ_s = 0.18081(11) J$, and the spin wave velocity $c = 1.6586(3) J a$ are determined with very high precision. Our study may serve as a test case for the comparison of lattice QCD Monte Carlo data with analytic predictions of the chiral effective theory for pions and nucleons, which is vital for the quantitative understanding of the strong interaction at low energies.

cond-mat.str-el↗
arXiv2010

Axial and electromagnetic observables of hyperons in 2-flavor chiral perturbation theory

Two-flavor chiral expansions provide a useful perturbative framework to study hadron properties. Such expansions should exhibit marked improvement over the conventional three-flavor chiral expansion. Although in principle one can formulate two-flavor theories for the various hyperon multiplets, the nearness of kaon thresholds can seriously undermine the effectiveness of such two-flavor theories in practice. We investigate the importance of virtual kaon thresholds on hyperon properties, specifically their isovector axial charges and electromagnetic observables. In particular we uncover the underlying expansion parameter governing the description of virtual kaon thresholds. For spin-half hyperons, this expansion parameter is under theoretical control. As a result, the virtual kaon contributions are well described in the two-flavor theory by terms analytic in the pion mass-squared. For spin three-half hyperons, however, one is closer to the kaon production threshold, and the expansion parameter is not as small. Breakdown of $SU(2)$ chiral perturbation theory is shown to arise from a pole in the expansion parameter associated with the kaon threshold. We find that, despite the fact that higher-order corrections to the expansion parameter is necessary to ascertain whether the two-flavor theory of spin three-half hyperons remains perturbative, there is a useful perturbative expansion for isovector axial charges and magnetic moments of both spin-half and spin three-half hyperons.

hep-lat↗
arXiv2010

Revisiting the Phase Transition of Spin-1/2 Heisenberg Model with a Spatially Staggered Anisotropy on the Square Lattice

Puzzled by the indication of a new critical theory for the spin-1/2 Heisenberg model with a spatially staggered anisotropy on the square lattice as suggested in \cite{Wenzel08}, we re-investigate the phase transition of this model induced by dimerization using first principle Monte Carlo simulations. We focus on studying the finite-size scaling of $ρ_{s1} L$ and $ρ_{s2} L$, where $L$ stands for the spatial box size used in the simulations and $ρ_{si}$ with $i \in \{1,2\}$ is the spin-stiffness in $i$-direction. From our Monte Carlo data, we find that $ρ_{s2} L$ suffers a much less severe correction compared to that of $ρ_{s1} L$. Therefore $ρ_{s2} L$ is a better quantity than $ρ_{s1} L$ for finite-size scaling analysis concerning the limitation of the availability of large volumes data in our study. Further, motivated by the so-called cubical regime in magnon chiral perturbation theory, we additionally perform a finite-size scaling analysis on our Monte Carlo data with the assumption that the ratio of spatial winding numbers squared is fixed through all simulations. As a result, the physical shape of the system remains fixed in our calculations. The validity of this new idea is confirmed by studying the phase transition driven by spatial anisotropy for the ladder anisotropic Heisenberg model. With this new strategy, even from $ρ_{s1} L$ which receives the most serious correction among the observables considered in this study, we arrive at a value for the critical exponent $ν$ which is consistent with the expected $O(3)$ value by using only up to $L = 64$ data points.

cond-mat.str-el↗
arXiv2010

A New Method of Calculating the Spin-Wave Velocity $c$ of Spin-1/2 Antiferromagnets With $O(N)$ Symmetry in a Monte Carlo Simulation

Motivated by the so-called cubical regime in magnon chiral perturbation theory, we propose a new method to calculate the low-energy constant, namely the spin-wave velocity $c$ of spin-1/2 antiferromagnets with $O(N)$ symmetry in a Monte Carlo simulation. Specifically we suggest that $c$ can be determined by $c = L/β$ when the squares of the spatial and temporal winding numbers are tuned to be the same in the Monte Carlo calculations. Here $β$ and $L$ are the inverse temperature and the box size used in the simulations when this condition is met. We verify the validity of this idea by simulating the quantum spin-1/2 XY model. The $c$ obtained by using the squares of winding numbers is given by $c = 1.1348(5)Ja$ which is consistent with the known values of $c$ in the literature. Unlike other conventional approaches, our new idea provides a direct method to measure $c$. Further, by simultaneously fitting our Monte Carlo data of susceptibilities $χ_{11}$ and spin susceptibilities $χ$ to their theoretical predictions from magnon chiral perturbation theory, we find $c$ is given by $c = 1.1347(2)Ja$ which agrees with the one we obtain by the new method of using the squares of winding numbers. The low-energy constants magnetization density ${\cal M}$ and spin stiffenss $ρ$ of quantum spin-1/2 XY model are determined as well and are given by ${\cal M} = 0.43561(1)/a^2$ and $ρ= 0.26974(5)J$, respectively. Thanks to the prediction power of magnon chiral perturbation theory which puts a very restricted constraint among the low-energy constants for the model considered here, the accuracy of ${\cal M}$ we present in this study is much precise than previous Monte Carlo result.

cond-mat.str-el↗
arXiv2009

The Phase Transition of the Spin-1/2 Heisenberg Model with a Spatially Staggered Anisotropy on the Square Lattice

Puzzled by the indication of a new critical theory for the spin-1/2 Heisenberg model with a spatially staggered anisotropy on the square lattice as suggested in \cite{Wenzel08}, we re-investigate the phase transition of this model induced by dimerization. We focus on studying the finite-size scaling of the observables $ρ_{s1} L$ and $ρ_{s2} L$, where $L$ stands for the spatial box sizes used in the simulations and $ρ_{si}$ with $i \in \{1,2\}$ is the spin-stiffness in $i$-direction. We find by performing finite-size scaling using the observable $ρ_{s2} L$, which corresponds to the spatial direction with a fixed antiferromagnetic coupling, one would suffer a much less severe correction compared to that of using $ρ_{s1} L$. Therefore $ρ_{s2} L$ is a better quantity than $ρ_{s1} L$ for finite-size scaling analysis concerning the limitation for the availability of large volumes data in our study. Remarkably, by employing the method of fixing the aspect-ratio of spatial winding numbers squared in the simulations, even from $ρ_{s1} L$ which receives the most serious correction among the observables considered in this study, we arrive at a value for the critical exponent $ν$ which is consistent with the expected O(3) value by using only up to $L = 64$ data points.

cond-mat.str-el↗
arXiv2009

Subtlety of Determining the Critical Exponent $ν$ of the Spin-1/2 Heisenberg Model with a Spatially Staggered Anisotropy on the Honeycomb Lattice

Puzzled by the indication of a new critical theory for the spin-1/2 Heisenberg model with a spatially staggered anisotropy on the square lattice as suggested in \cite{Wenzel08}, we study a similar anisotropic spin-1/2 Heisenberg model on the honeycomb lattice. The critical point where the phase transition occurs due to the dimerization as well as the critical exponent $ν$ are analyzed in great detail. Remarkly, using most of the available data points in conjunction with the expected finite-size scaling ansatz with a sub-leading correction indeed leads to a consistent $ν= 0.691(2)$ with that calculated in \cite{Wenzel08}. However by using the data with large number of spins $N$, we obtain $ν= 0.707(6)$ which agrees with the most accurate Monte Carlo O(3) value $ν= 0.7112(5)$ as well.

cond-mat.str-el↗