Two scenarios of the quantum critical point

Two different scenarios of the quantum critical point (QCP), a zero-temperature instability of the Landau state related to the divergence of the effective mass, are investigated. Flaws of the standard scenario of the QCP, where this divergence is attributed to the occurrence of some second-order phase transition, are demonstrated. Salient features of a different topological scenario of the QCP, associated with the emergence of bifurcation points in the equation ∈(p) = μ that ordinarily determines the Fermi momentum, are analyzed. The topological scenario of the QCP is applied to three-dimensional (3D) Fermi liquids with an attractive current-current interaction. The text was submitted by the author in English.     

Two scenarios of the quantum critical point

Two different scenarios of the quantum critical point (QCP), a zero-temperature instability of the Landau state related to the divergence of the effective mass, are investigated. Flaws of the standard scenario of the QCP, where this divergence is attributed to the occurrence of some second-order phase transition, are demonstrated. Salient features of a different topological scenario of the QCP, associated with the emergence of bifurcation points in the equation ∈(p) = μ that ordinarily determines the Fermi momentum, are analyzed. The topological scenario of the QCP is applied to three-dimensional (3D) Fermi liquids with an attractive current-current interaction.     

Adaptation of the Landau-Migdal quasiparticle pattern to strongly correlated Fermi systems

A quasiparticle pattern advanced in Landau’s first article on Fermi-liquid theory is adapted to elucidate the properties of a class of strongly correlated Fermi systems characterized by a Lifshitz phase diagram featuring a quantum critical point (QCP) where the density of states diverges. The necessary condition for stability of the Landau Fermi-Liquid state is shown to break down in such systems, triggering a cascade of topological phase transitions that lead, without symmetry violation, to states with multi-connected Fermi surfaces. The end point of this evolution is found to be an exceptional state whose spectrum of single-particle excitations exhibits a completely flat portion at zero temperature. Analysis of the evolution of the temperature dependence of the single-particle spectrum yields results that provide a natural explanation of classical behavior of this class of Fermi systems in the QCP region.     

Fermi surface reconstruction by dynamic magnetic fluctuations

We demonstrate that nearly critical quantum magnetic fluctuations in strongly correlated electron systems can change the Fermi surface topology and also lead to spin charge separation in two dimensions. To demonstrate these effects, we consider a small number of holes injected into the bilayer antiferromagnet. The system has a quantum critical point (QCP) which separates magnetically ordered and disordered phases. We demonstrate that in the physically interesting regime, there is a magnetically driven Lifshitz point (LP) inside the magnetically disordered phase. At the LP, the topology of the hole Fermi surface is changed. We also demonstrate that in this regime, the hole spin and charge necessarily separate when approaching the QCP. The considered model sheds light on generic problems concerning the physics of the cuprates.     

Universal scaling and a novel quantum critical behavior of CeRhSb1-xSnx

We observe and explain a universal scaling rhochi = const for the electrical resistivity rho with the inverse magnetic susceptibility chi(-1) for the Kondo insulator CeRhSb(1-x)Snx. In the regime where the Kondo gap disappears (x > 0.12), the system forms a non-Fermi liquid (NFL), which transforms into a Fermi liquid at higher temperature. The NFL behavior is associated with the presence of a novel quantum critical point (QCP) at the Kondo insulator-correlated metal boundary. The divergent behavior of the resistivity, the susceptibility, and the specific heat has been observed when approaching the QCP from the metallic side and is interpreted as due to the competition between the Kondo and the intersite magnetic correlations.     

Field-induced quantum critical point in CeCoIn5

The resistivity of the heavy-fermion superconductor CeCoIn5 was measured as a function of temperature, down to 25 mK and in magnetic fields of up to 16 T applied perpendicular to the basal plane. With increasing field, we observe a suppression of the non-Fermi liquid behavior, rho approximately T, and the development of a Fermi liquid state, with its characteristic rho=rho(0)+AT2 dependence. The field dependence of the T2 coefficient shows critical behavior with an exponent of 1.37. This is evidence for a field-induced quantum critical point (QCP), occurring at a critical field which coincides, within experimental accuracy, with the superconducting critical field H(c2). We discuss the relation of this field-tuned QCP to a change in the magnetic state, seen as a change in magnetoresistance from positive to negative, at a crossover line that has a common border with the superconducting region below approximately 1 K.     

Charge redistribution and a shortening of the Fe—As bond at the quantum critical point of SmO1–xFxFeAs

Many researchers have pointed out that there is a quantum critical point (QCP) in the F‐doped SmOFeAs system. In this paper, the electronic structure and local structure of the superconductive FeAs layer in SmO_1–xF_xFeAs as a function of the F‐doping concentration have been investigated using Fe and As K‐edge X‐ray absorption spectroscopy. Experiments performed on the X‐ray absorption near‐edge structure showed that in the vicinity of the QCP the intensity of the pre‐edge feature at the Fe‐edge decreases continuously, while there is a striking rise of the shoulder‐peak at the As edge, suggesting the occurrence of charge redistribution near the QCP. Further analysis on the As K‐edge extended X‐ray absorption fine structure demonstrated that the charge redistribution originates mostly from a shortening of the Fe—As bond at the QCP. An evident relationship between the mysterious QCP and the fundamental Fe—As bond was established, providing new insights on the interplay between QCP, charge dynamics and the local structural Fe—As bond in Fe‐based superconductors.     

Interplay between unconventional superconductivity and heavy-fermion quantum criticality: CeCu2Si2 versus YbRh2Si2

In this paper the low-temperature properties of two isostructural canonical heavy-fermion compounds are contrasted with regards to the interplay between antiferromagnetic (AF) quantum criticality and superconductivity. For CeCu₂Si₂, fully-gapped d-wave superconductivity forms in the vicinity of an itinerant three-dimensional heavy-fermion spin-density-wave (SDW) quantum critical point (QCP). Inelastic neutron scattering results highlight that both quantum critical SDW fluctuations as well as Mott-type fluctuations of local magnetic moments contribute to the formation of Cooper pairs in CeCu₂Si₂. In YbRh₂Si₂, superconductivity appears to be suppressed at T???10?mK by AF order (T_N?=?70?mK). Ultra-low temperature measurements reveal a hybrid order between nuclear and 4f-electronic spins, which is dominated by the Yb-derived nuclear spins, to develop at T_A slightly above 2?mK. The hybrid order turns out to strongly compete with the primary 4f-electronic order and to push the material towards its QCP. Apparently, this paves the way for heavy-fermion superconductivity to form at T_c?=?2?mK. Like the pressure – induced QCP in CeRhIn₅, the magnetic field – induced one in YbRh₂Si₂ is of the local Kondo-destroying variety which corresponds to a Mott-type transition at zero temperature. Therefore, these materials form the link between the large family of about fifty low-T unconventional heavy – fermion superconductors and other families of unconventional superconductors with higher T_cs, notably the doped Mott insulators of the cuprates, organic charge-transfer salts and some of the Fe-based superconductors. Our study suggests that heavy-fermion superconductivity near an AF QCP is a robust phenomenon.     

Superconductivity in CeCoIn5-xSnx: veil over an ordered state or novel quantum critical point?

Measurements of specific heat and electrical resistivity in magnetic fields up to 9 T along [001] and temperatures down to 50 mK of Sn-substituted CeCoIn5 are reported. The maximal -ln(T) divergence of the specific heat at the upper critical field Hc2 down to the lowest temperature characteristic of non-Fermi-liquid systems at the quantum critical point (QCP), the universal scaling of the Sommerfeld coefficient, and agreement of the data with spin-fluctuation theory provide strong evidence for quantum criticality at Hc2 for all x< or =0.12 in CeCoIn5-xSnx. These results indicate the "accidental" coincidence of the QCP located near Hc2 in pure CeCoIn5, in actuality, constitute a novel quantum critical point associated with unconventional superconductivity.     

Evidence for the strain critical point in high Tc superconductors

We report experimental evidence for the phase diagram of doped cuprate superconductors as a function of the micro-strain of the planar Cu-O bond length, measured by Cu K-edge EXAFS, and hole doping . The local lattice distortions are measured by EXAFS and the charge ordering is measured by synchrotron radiation diffuse X-ray diffraction. This phase diagram shows a QCP at P() where for charge-orbital-spin stripes and free carriers co-exist. The superconducting phase occurs in the region of critical fluctuations around this QCP. The function of two variables shows its maximum at the strain QCP. The critical fluctuations near this strain QCP give the self-organization of a metallic superlattice of quantum wires “superstripes" that favors the amplification of the critical temperature. Received 25 September 2000     

Scaling functions for classical to quantum crossover in the transverse Ising model via an effective Wilsonian renormalization group approach in 4 – ε dimensions

The classical to quantum crossover, which occurs in d-dimensional transverse field Ising model-like systems decreasing the temperature to zero in the influence domain of the quantum critical point (QCP), is described by employing an effective Wilsonian renormalization group approach in 4 - ε dimensions. The basic ingredient of the treatment is the static action arising from a preliminary one-loop averaging over non-zero frequency modes, which enter the original quantum one. The crossover scaling functions for susceptibility and related thermodynamic quantities are obtained to first order in ε as explicit functions of the temperature and the applied magnetic field. In our static framework, which can be easily extended to other quantum systems exhibiting a critical line which terminates in a QCP, the suitable procedure for observing this type of crossover through genuine thermodynamic measurements is clarified consistently with available experiments. Remarkably, our basic idea and results may be usefully employed to explore also the dimensional crossover which takes place in classical Ising-like systems with slab or film geometry and, possibly, in other finite-size classical systems.     

Grüneisen ratio quest for self-duality of quantum criticality in a spin-1/2 XY chain with Dzyaloshinskii–Moriya interaction

The quantum phase transition(QPT) and quantum criticality of an anisotropic spin-1/2 XY chain under the interplay of magnetic field and Dzyaloshinskii–Moriya(DM) interaction, which is interpreted as an electric field, are investigated, wherein the anisotropic parameter plays a similar role as the superconducting pairing gap in the interacting Kitaev topological superconductor model that protects the topological order. It is shown that the thermal Drude weight is a good quantity to characterize the gapped(D_(th) = 0) and gapless(D_(th) 0) ground states. The continuous QPT is marked by a quantum critical point(QCP) associated with entropy accumulation, which is manifested by a characteristic Güneisen ratio(GR) with or without selfduality symmetry. It is shown that at a self-dual QCP, the GR keeps a finite value as T→0,while at a general QCP without self-duality symmetry, it displays a power-law temperature dependent divergence: Γ(T,r_c)～±T~(-1),which provides a novel thermodynamic means for probing QPT.     

Interplay of Quantum and Classical Fluctuations Near Quantum Critical Points

For a system near a quantum critical point (QCP), above its lower critical dimension d _L , there is in general a critical line of second-order phase transitions that separates the broken symmetry phase at finite temperatures from the disordered phase. The phase transitions along this line are governed by thermal critical exponents that are different from those associated with the quantum critical point. We point out that, if the effective dimension of the QCP, d _eff?=?d?+?z (d is the Euclidean dimension of the system and z the dynamic quantum critical exponent) is above its upper critical dimension $d_{_{C}}$ there is an intermingle of classical (thermal) and quantum critical fluctuations near the QCP. This is due to the breakdown of the generalized scaling relation ψ?=?νz between the shift exponent ψ of the critical line and the crossover exponent νz, for $d+z>d_{_{C}}$ by a dangerous irrelevant interaction. This phenomenon has clear experimental consequences, like the suppression of the amplitude of classical critical fluctuations near the line of finite temperature phase transitions as the critical temperature is reduced approaching the QCP.     

Possible quantum critical point in La(2/3)Ca(1/3)Mn(1-x)Ga x O3

We study the magnetic ground state in La(2/3)Ca(1/3)Mn(1-x)Ga x O3 manganites, where a quantum critical point (QCP) has been theoretically predicted. The metallic ferromagnetic ground state for low Ga doping breaks down for x > or = 0.11, an insulating state being established at low temperatures. Long-range ferromagnetism coexists with short-range magnetic correlations in the concentration range 0.11 < or = x < or = 0.145 while only the short-range correlations survive for x > or = 0.16. We discuss the implications of such a QCP to the physics of manganites and compare to other QCP systems.     

Magnetic-field control of quantum critical points of valence transition

We study the mechanism of how critical end points of first-order valence transitions are controlled by a magnetic field. We show that the critical temperature is suppressed to be a quantum critical point (QCP) by a magnetic field, and unexpectedly, the QCP exhibits nonmonotonic field dependence in the ground-state phase diagram, giving rise to the emergence of metamagnetism even in the intermediate valence-crossover regime. The driving force of the field-induced QCP is clarified to be cooperative phenomena of the Zeeman and Kondo effects, which create a distinct energy scale from the Kondo temperature. This mechanism explains the peculiar magnetic response in CeIrIn(5) and the metamagnetic transition in YbXCu(4) for X=In as well as the sharp contrast between X=Ag and Cd.     

Logarithmic terms in entanglement entropies of 2D quantum critical points and Shannon entropies of spin chains

Universal logarithmic terms in the entanglement entropy appear at quantum critical points (QCPs) in one dimension (1D) and have been predicted in 2D at QCPs described by 2D conformal field theories. The entanglement entropy in a strip geometry at such QCPs can be obtained via the "Shannon entropy" of a 1D spin chain with open boundary conditions. The Shannon entropy of the XXZ chain is found to have a logarithmic term that implies, for the QCP of the square-lattice quantum dimer model, a logarithm with universal coefficient ±0.25. However, the logarithm in the Shannon entropy of the transverse-field Ising model, which corresponds to entanglement in the 2D Ising conformal QCP, is found to have a singular dependence on the replica or Rényi index resulting from flows to different boundary conditions at the entanglement cut.     

Multiband nodeless superconductivity near the charge-density-wave quantum critical point in ZrTe_(3-x)Se_x

It was found that selenium doping can suppress the charge-density-wave(CDW) order and induce bulk superconductivity in ZrTe_3. The observed superconducting dome suggests the existence of a CDW quantum critical point(QCP) in ZrTe_3-xSex near x ≈ 0.04. To elucidate the superconducting state near the CDW QCP, we measure the thermal conductivity of two ZrTe_(3-x)Se_x single crystals(x = 0.044 and 0.051) down to 80 m K. For both samples, the residual linear term κ_0/T at zero field is negligible, which is a clear evidence for nodeless superconducting gap. Furthermore, the field dependence of κ_0/T manifests a multigap behavior. These results demonstrate multiple nodeless superconducting gaps in ZrTe_(3-x)Se_x,which indicates conventional superconductivity despite of the existence of a CDW QCP.     

铁基超导体的量子临界行为

铁基超导体呈现丰富的电子相图, 各种有序态相互交叠. 本文主要介绍利用核磁共振手段在空穴型和电子型掺杂的BaFe₂As₂以及LaFeAsO_1-xF_x这三种具有代表性的铁基超导体中探测到的反铁磁序与超导序的微观共存、量子临界点和量子临界行为. 实验发现, 无论在空穴型还是电子型掺杂的铁基超导体中, 反铁磁相变温度都随着掺杂被抑制, 并最终在某个掺杂量降到零温而形成量子临界点. 在反铁磁转变温度之上存在结构相变, 其转变温度也随着掺杂而降低. 核磁共振谱证实结构相变也形成一个量子临界点. 本文介绍核磁共振及输运测量揭示的这两种量子临界点附近存在的量子临界行为, 共存态下奇异的超导性质等.     

用量子蒙特卡罗方法研究二维超流-莫特绝缘体相变点附近的希格斯粒子

与伽利略不变性的超流体不同, 具有洛伦兹不变性的超流体中除了声子模之外, 还存在希格斯振幅模(Higgs amplitude mode). 在二维情况下, 由于存在十分剧烈的衰变成声子模的过程, 希格斯模是否仍然是一个能产生尖锐线性响应的激发子成为了一个问题. 近年来的进展最终对这一持续数十年的争论做出了肯定的回答, 证实了希格斯的可观测性. 在这里, 我们回顾一系列的数值方面的工作; 它们以二维超流体(superfluid)到莫特绝缘体(Mott insulator) 量子相变点(SF-MI QCP) 附近的具有洛伦兹不变性的超流体为对象, 成功探测到了希格斯模的线性响应信号. 特别是, 我们介绍了一种如何使用平衡态系统的蒙特卡罗算法计算强关联系统的延迟响应函数(retarded response function)的方法. 该方法主要包含两个核心步骤: 即通过路径积分表示下的蠕虫算法这一高效的蒙特卡罗算法计算平衡态系统的虚时间关联函数, 然后利用数值解析延拓方法从虚时间关联函数中获得实时间(实频率)的响应函数. 将该数值方法应用于二维SF-MI QCP附近的玻色-哈伯德模型(Bose-Hubbard Model), 结果表明尽管在超流相中, 希格斯模衰变过程非常剧烈, 但是在动能算符相对应的延迟响应函数的虚部中, 仍然可以观测到希格斯模所对应的尖锐的共振峰. 进一步的研究表明, 在莫特绝缘相, 甚至常流体相中, 也可能存在类似的共振峰信号. 由于可以在光晶格中超冷原子系统等凝聚态中观测到SF-MI QCP, 因此希格斯共振峰有望通过实验进行直接探测. 此外我们指出, 同样的希格斯共振峰还存在于所有和SF-MI QCP具有相同普适类((2+1)维相对论性U(1)临界性)的量子临界系统中.     

Understanding the heavy fermion phenomenology from a microscopic model

We solve the 3D periodic Anderson model using a two impurity cluster dynamical mean field theory. We obtain the temperature versus hybridization phase diagram. Approaching the quantum critical point (QCP) both the Néel and lattice Kondo temperatures decrease and they do not cross at the lowest temperature we reached. While strong ferromagnetic spin fluctuation on the Kondo side is observed, our result suggests the critical static spin susceptibility is local in space at the QCP. We observe in the crossover region a logarithmic temperature dependence in the specific heat coefficient and spin susceptibility.