Using the tensor renormalization group method based on the higher-order singular value decomposition, we have studied the phase transitions of the five-state clock model on the square lattice. The temperature dependen...Using the tensor renormalization group method based on the higher-order singular value decomposition, we have studied the phase transitions of the five-state clock model on the square lattice. The temperature dependence of the specific heat indicates the system has two phase transitions, as verified clearly by the correlation function at three representative tem- peratures. By calculating the magnetic susceptibility, we obtained only the upper critical temperature as To2 = 0.9565（7）. Investigating the fixed-point tensor, we precisely locate the transition temperatures at Tcl = 0.9029（1） and Tc2 = 0.9520（1）, consistent well with the Monte Carlo and the density matrix renormalization group results.展开更多
Density order is usually a consequence of the competition between long-range and short-range interactions.Here we report a density ordered superfluid emergent from a homogeneous Mott insulator due to the competition b...Density order is usually a consequence of the competition between long-range and short-range interactions.Here we report a density ordered superfluid emergent from a homogeneous Mott insulator due to the competition between frustrations and local interactions.This transition is found in a Bose–Hubbard model on a frustrated triangle lattice with an extra pairing term.Furthermore,we find a quantum phase transition between two different density ordered superfluids,which is beyond the Landau–Ginzburg(LG)paradigm.A U(1)symmetry is emergent at the critical point,while the symmetry in each density ordered superfluid is Z_(2)×Z_(3).We call the transition a‘shamrock transition’,due to its degenerate ground state in the parameter space being a shamrock-like curve rather than a circle in an LG-type transition.Effective low energy theories are established for the two transitions mentioned above and we find their resemblance and differences with clock models.展开更多
A new Precise Point Positioning(PPP)service,called the PPP-B2b service,has been implemented in the BeiDou-3 Navigation Satellite System(BDS-3),which brings new opportunities for time transfer.However,the solution usin...A new Precise Point Positioning(PPP)service,called the PPP-B2b service,has been implemented in the BeiDou-3 Navigation Satellite System(BDS-3),which brings new opportunities for time transfer.However,the solution using the traditional PPP method with the PPP-B2b correction still absorbs some unknown errors and needs reconverging when there exist abnormal data.We developed a new receiver clock model to improve PPP time transfer using the PPP-B2b correction.The traditional PPP time transfers using PPP-B2b with BDS-3,Global Positioning System(GPS),and BDS-3/GPS(Scheme1)are compared with the corresponding time transfer with the proposed clock model(Scheme2).The results show that GPS-only PPP is not recommended because of low accuracy of 2 ns.BDS-3 or BDS-3/GPS PPP time transfers in Scheme1 can realize about 0.2 ns accuracy.When the new clock model is applied,the accuracy can be improved by up to 45%and 39.8%for BDS-3 and BDS-3/GPS PPP,respectively.The proposed clock model can signifcantly improve the short-term frequency stability by 57.4%,but less for the long-term stability.展开更多
The process to achieve time synchronization and ranging for a network of mobile nodes is raising a concern among researchers, and hence a variety of joint time synchronization and ranging algorithms have been proposed...The process to achieve time synchronization and ranging for a network of mobile nodes is raising a concern among researchers, and hence a variety of joint time synchronization and ranging algorithms have been proposed in recent years. However, few of them handle the case of all-node motion under unknown positions and velocities. This study addresses the problem of determining ranging and time synchronization for a group of nodes moving within a local area. First, we examined several models of clock discrepancy and synchronous two-way ranging. Based upon these models, we present a solution for time synchronization with known positions and velocities. Next, we propose a functional model that jointly estimates the clock skew, clock offset, and time of flight in the absence of a priori knowledge for a pair of mobile nodes. Then, we extend this model to a network-wide time synchronization scheme by way of a global least square estimator. We also discuss the advantages and disadvantages of our model compared to the existing algorithms, and we provide some applicable scenarios as well. Finally, we show that the simulation results verify the validity of our analysis.展开更多
基金Project supported by the Fundamental Research Funds for the Central Universities,China(Grant No.531107040857)the Natural Science Foundation of Hunan Province,China(Grant No.851204035)the National Natural Science Foundation of China(Grant No.11774420)
文摘Using the tensor renormalization group method based on the higher-order singular value decomposition, we have studied the phase transitions of the five-state clock model on the square lattice. The temperature dependence of the specific heat indicates the system has two phase transitions, as verified clearly by the correlation function at three representative tem- peratures. By calculating the magnetic susceptibility, we obtained only the upper critical temperature as To2 = 0.9565（7）. Investigating the fixed-point tensor, we precisely locate the transition temperatures at Tcl = 0.9029（1） and Tc2 = 0.9520（1）, consistent well with the Monte Carlo and the density matrix renormalization group results.
基金supported by the Beijing Natural Science Foundation(Z180013)(YC)National Natural Science Foundation of China(NSFC)under Grant No.12174358(YC)and No.11734010(YC and CW)MOST Grant No.2016YFA0301600(CW)。
文摘Density order is usually a consequence of the competition between long-range and short-range interactions.Here we report a density ordered superfluid emergent from a homogeneous Mott insulator due to the competition between frustrations and local interactions.This transition is found in a Bose–Hubbard model on a frustrated triangle lattice with an extra pairing term.Furthermore,we find a quantum phase transition between two different density ordered superfluids,which is beyond the Landau–Ginzburg(LG)paradigm.A U(1)symmetry is emergent at the critical point,while the symmetry in each density ordered superfluid is Z_(2)×Z_(3).We call the transition a‘shamrock transition’,due to its degenerate ground state in the parameter space being a shamrock-like curve rather than a circle in an LG-type transition.Effective low energy theories are established for the two transitions mentioned above and we find their resemblance and differences with clock models.
基金the National Natural Science Foundation of China(Nos.42104014,42077003,41904018)Natural Science Foundation of the Higher Education Institutions of Jiangsu Province,China(21KJB420005)State Key Laboratory of Geodesy and Earth’s Dynamics(SKLGED2022-3-6)and Highlevel innovation and entrepreneurship talent plan of Jiangsu Province.
文摘A new Precise Point Positioning(PPP)service,called the PPP-B2b service,has been implemented in the BeiDou-3 Navigation Satellite System(BDS-3),which brings new opportunities for time transfer.However,the solution using the traditional PPP method with the PPP-B2b correction still absorbs some unknown errors and needs reconverging when there exist abnormal data.We developed a new receiver clock model to improve PPP time transfer using the PPP-B2b correction.The traditional PPP time transfers using PPP-B2b with BDS-3,Global Positioning System(GPS),and BDS-3/GPS(Scheme1)are compared with the corresponding time transfer with the proposed clock model(Scheme2).The results show that GPS-only PPP is not recommended because of low accuracy of 2 ns.BDS-3 or BDS-3/GPS PPP time transfers in Scheme1 can realize about 0.2 ns accuracy.When the new clock model is applied,the accuracy can be improved by up to 45%and 39.8%for BDS-3 and BDS-3/GPS PPP,respectively.The proposed clock model can signifcantly improve the short-term frequency stability by 57.4%,but less for the long-term stability.
基金supported by the National Natural Science Foundation of China(Grant No.61471021)
文摘The process to achieve time synchronization and ranging for a network of mobile nodes is raising a concern among researchers, and hence a variety of joint time synchronization and ranging algorithms have been proposed in recent years. However, few of them handle the case of all-node motion under unknown positions and velocities. This study addresses the problem of determining ranging and time synchronization for a group of nodes moving within a local area. First, we examined several models of clock discrepancy and synchronous two-way ranging. Based upon these models, we present a solution for time synchronization with known positions and velocities. Next, we propose a functional model that jointly estimates the clock skew, clock offset, and time of flight in the absence of a priori knowledge for a pair of mobile nodes. Then, we extend this model to a network-wide time synchronization scheme by way of a global least square estimator. We also discuss the advantages and disadvantages of our model compared to the existing algorithms, and we provide some applicable scenarios as well. Finally, we show that the simulation results verify the validity of our analysis.
