Rich Quantum Phase Transitions In Several Extended Spin-boson Models

The spin-boson model is a paradigmatic one in condensed matter physics,light-matter interaction systems,and open quantum systems.The quantum phase transition(QPT)in this model has always been the hot topic for a long time in many physics fields.In this Ph.D thesis,we studied the rich QPTs and the phase diagrams of several extended spin-boson models where anisotropic couplings between system and bath,the antiferromagnetic bias field,the complex interactions between spins are considered individually,which could be realized experimentally using different manipulated approaches in advanced solid devices.We describe our theoretical results in four parts in detail below:First,we study the spin-boson model without the counterrotating terms by a numerically exact method based on variational matrix product states(VPMS).We find that the second-order QPT for the sub-Ohmic bath always occurs,no matter whether the counterrotating coupling terms appear or not.And the criticality is only the bath exponent dependent.For large bath exponents,both the first-and the second-order QPTs take place in the same model.This unex-pected second-order QPT is further confirmed by multi-coherent-state(MCS)variational stud-ies,while the first-order QPT is corroborated with the exact diagonalization in the truncated Hilbert space(NED).When extended to the Ohmic bath,many first-order QPTs appear succes-sively in a wide coupling regime,in contrast to previous findings.Second,we study the phase diagrams and QPTs in the anisotropic spin-boson model.The parity,the order parameter,and the entanglement between the two-level system and the bosonic bath in the ground-state are calculated using VMPS approach.Rich quantum phases are re-vealed:the delocalized phase with even parity(?),the delocalized phase with odd parity having the high entanglement between system and bath(?),and the localized phase with broken sym-metry(?).The quantum tricritical point is detected by the intersection of three phase bound-aries.Due to the competition of phase ? and ?,although the localized phase dominates in the low bath exponent and at strong coupling,there still exists highly entangled regions where order parameters are suppressed into local minimum.Moreover,for moderate anisotropic case,it experiences phases(?)(?)(?)(?)successively,resulting in the unusual reentrance to the lo-calized phase and several second-order QPTs.This novel phenomena have been never found in the other light-matter interaction systems.Then we turn to the spin-boson model with two dissipative spins in an antiferromagnetic bias field.In the sub-Ohmic case,we calculate several observables in the ground-state,such as the order parameter and the entropy by VMPS approach.We indeed find the existence of novel tricritical point,where the second-order QPT meets the first-order one,in this model.The phase boundary can be also determined by the change of the entropy,the first and second derivative of energy.For the Ohmic bath,the Kosterlitz-Thouless(KT)phase transition can be directly driven into first-order QPT by the antiferromagnetic bias field.Finally,we consider the extended two-spin spin-boson model with the XY-type spin in-teraction.In Dicke-Ising and two-spin spin-boson models,the XX-type spin interaction could drastically change the types of the QPTs.If competitive YY-type interaction is added simul-taneously,the total angular momentum j of system is no longer conserved,which may lead to novel QPTs and richer phase diagrams by adjusting the strength of both XX-and YY-type inter-action.In the sub-Ohmic bath,by calculating the parity,the order parameter,the total angular momentum,and the entropy using VMPS,we discover four quantum phases:odd parity phase with j=1(?),even parity phase with j=1(?),odd parity phase with j=0(?),and delocalized phase with j=1(?).These phases are separated by two second-order QPT boundaries and three first-order QPT boundaries.Two tricritical points are located,respectively,in subspace K<0 and K>0 where K is the strength of XX-and YY-type spin interaction.Richer quantum phase transitions can appear in the phase diagram,even for the Ohmic bath where the KT QPT and first-order QPTs are present in some parameter space.All above extended spin-boson models could be realized in the superconducting circuit QED system and trapped ions.We believe that those models would serve as new important labs to study the rich quantum criticality and the novel quantum tricritical point.