Anatomy of quantum critical wave functions in dissipative impurity problems

Blunden-Codd, Zach; Bera, Soumya; Bruognolo, Benedikt; Linden, Nils-Oliver; Chin, Alex W.; Delft, Jan von; Nazir, Ahsan; Florens, Serge

doi:10.1103/physrevb.95.085104

Cited by 34 publications

(34 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As one of successful approaches that enables direct access to the ground-state wave function, the variational method has recently been adopted to study SBM, where the form of the trial wave function plays a vital role in obtaining the ground state [29,42,46]. In this work, a systematic coherent-state expansion, termed as the "multi-D 1 ansatz", is used as the variational ansatz, which has been proved to be efficient in tackling the ground-state phase transitions and quantum dynamics of SBM and its variant [29,30,48],…”

Section: Model and Methodsmentioning

confidence: 99%

Variational Study of the Two‐Impurity Spin–Boson Model with a Common Ohmic Bath: Ground‐State Phase Transitions

et al. 2018

View full text Add to dashboard Cite

By means of a trial wave function, the multi-D 1 ansatz, extensive variational calculations with more than ten thousand parameters have been carried out to study quantum phase transitions in the ground states of a twoimpurity system embedded in a common Ohmic bath of bosons. Quantum criticality in both the impurity system and the Ohmic bosonic bath is investigated with relevant transition points and critical exponents determined accurately. With the linear grid of the Ohmic spectral density, our numerical calculations produce a much better description of the ground states with lower energies than other calculations employing a logarithmic grid with a discretization factor far greater than unity. It offers a possible solution to the considerable controversy on the critical coupling in the literature. Moreover, the ground-state phase transition is inferred to be of first order in the presence of strong antiferromagnetic spinspin coupling, at variance with that in the ferromagnetic regime or in the absence of spin-spin coupling where the transition belongs to the Kosterlitz-Thouless

show abstract

Section: Model and Methodsmentioning

confidence: 99%

Variational Study of the Two‐Impurity Spin–Boson Model with a Common Ohmic Bath: Ground‐State Phase Transitions

et al. 2018

View full text Add to dashboard Cite

show abstract

“…All these findings in the MCS variational study provide strong evidence of the second-order QPT in the spin-boson model with RWA. As found recently by Blunden-Codd et al [32] that a very accurate wave function can be only obtained by at least 100 coherent states, by N c = 6 coherent states the MCS results for the order parameter and energy still slightly deviate from those by VMPS above the critical points.…”

Section: Evidence For the Second-order Qpt By Mcs Variational Studiesmentioning

confidence: 59%

Quantum phase transitions in the spin-boson model without the counterrotating terms

Wang

Duan

et al. 2019

Phys. Rev. B

View full text Add to dashboard Cite

We study the spin-boson model without the counterrotating terms by a numerically exact method based on variational matrix product states. Surprisingly, the second-order quantum phase transition (QPT) is observed for the sub-Ohmic bath in the rotating-wave approximations. Moreover, firstorder QPTs can also appear before the critical points. With the decrease of the bath exponents, these first-order QPTs disappear successively, while the second-order QPT remains robust. The secondorder QPT is further confirmed by multi-coherent-states variational studies, while the first-order QPT is corroborated with the exact diagonalization in the truncated Hilbert space. Extension to the Ohmic bath is also performed, and many first-order QPTs appear successively in a wide coupling regime, in contrast to previous findings. The previous pictures for many physical phenomena for the spin-boson model in the rotating-wave approximation have to be modified at least at the strong coupling.

show abstract

“…As mentioned above, most analytical predictions for the SBM are obtained deep in the scaling limit, while numerical results necessarily involve only moderately large values of

. When comparing results, it is common in the literature to evaluate analytical expressions with a re-scaled coupling strength

to account for this [ 45 , 46 , 47 ], which we have applied in Figure 5 . We found that a constant factor

gave excellent agreement across the parameter space for both one and two-bath SBMs, as shown in the inset of Figure 5 .…”

Section: Resultsmentioning

confidence: 99%

Matrix Product State Simulations of Non-Equilibrium Steady States and Transient Heat Flows in the Two-Bath Spin-Boson Model at Finite Temperatures

Dunnett

Chin

2021

Entropy

Self Cite

View full text Add to dashboard Cite

Simulating the non-perturbative and non-Markovian dynamics of open quantum systems is a very challenging many body problem, due to the need to evolve both the system and its environments on an equal footing. Tensor network and matrix product states (MPS) have emerged as powerful tools for open system models, but the numerical resources required to treat finite-temperature environments grow extremely rapidly and limit their applications. In this study we use time-dependent variational evolution of MPS to explore the striking theory of Tamascelli et al. (Phys. Rev. Lett. 2019, 123, 090402.) that shows how finite-temperature open dynamics can be obtained from zero temperature, i.e., pure wave function, simulations. Using this approach, we produce a benchmark dataset for the dynamics of the Ohmic spin-boson model across a wide range of coupling strengths and temperatures, and also present a detailed analysis of the numerical costs of simulating non-equilibrium steady states, such as those emerging from the non-perturbative coupling of a qubit to baths at different temperatures. Despite ever-growing resource requirements, we find that converged non-perturbative results can be obtained, and we discuss a number of recent ideas and numerical techniques that should allow wide application of MPS to complex open quantum systems.

show abstract

Anatomy of quantum critical wave functions in dissipative impurity problems

Cited by 34 publications

References 38 publications

Variational Study of the Two‐Impurity Spin–Boson Model with a Common Ohmic Bath: Ground‐State Phase Transitions

Variational Study of the Two‐Impurity Spin–Boson Model with a Common Ohmic Bath: Ground‐State Phase Transitions

Quantum phase transitions in the spin-boson model without the counterrotating terms

Matrix Product State Simulations of Non-Equilibrium Steady States and Transient Heat Flows in the Two-Bath Spin-Boson Model at Finite Temperatures

Contact Info

Product

Resources

About