Quantum Critical Point
Encyclopedia
A quantum critical point is a special class of continuous phase transition
that takes place at the absolute zero
of temperature, typically in a material where the phase transition temperature has been driven to zero by the application of a pressure, field or through doping.
Conventional phase transitions occur at finite temperature, when the growth of random thermal fluctuations
leads to a
change in the physical state of a system. Condensed matter physics
research over the past few decades has revealed a new class of phase transitions, called a quantum phase transition
, which take place at absolute zero
, and which are
driven by the zero point quantum fluctuations associated with Heisenberg's uncertainty principle
.
where a second-order transition occurs the critical fluctuations are scale invariant and extend over the entire system. At a finite temperature phase transition, the fluctuations that develop at a critical point are governed by classical physics, because the characteristic energy of quantum fluctuations is always smaller than the characteristic Boltzmann thermal energy
.
At a quantum critical point, the critical fluctuations are quantum mechanical in nature, exhibiting scale invariance in both space and in time. Unlike classical critical points, where the critical fluctuations are limited to a narrow region around the phase transition, the influence of a quantum critical point is felt over a wide range of temperatures above the quantum critical point, so the effect of quantum criticality is felt without ever reaching absolute zero. Quantum criticality was first observed in ferroelectrics
, in which the ferroelectric transition temperature is suppressed to zero.
A wide variety of metallic ferromagnets
and antiferromagnets
have been observed to develop quantum critical behavior when their magnetic transition temperature is driven to zero through the application of pressure, chemical doping or magnetic fields. In these cases, the properties of the metal are radically transformed by the critical fluctuations, departing qualitatively from the standard Fermi liquid
behavior, to form a metallic state sometimes called a non-Fermi liquid or a "strange metal". There is particular interest in these unusual metallic states, which are believed to exhibit a marked preponderence towards the development of superconductivity
.
.
A quantum critical endpoint arises when a finite temperature critical point is tuned to zero temperature. One of the best studied examples occurs in the layered ruthenate metal, Sr3Ru2O7 in a magnetic field. This material shows metamagnetism
with a low-temperature first-order metamagnetic transition where the magnetization jumps when a magnetic field is applied within the directions of the layers. The first-order jump terminates in a critical endpoint at about 1 kelvin. By switching the direction of the magnetic field so that it points almost perpendicular to the layers, the critical endpoint is tuned to zero temperature at a field of about 8 teslas. The resulting quantum critical fluctuations dominate the physical properties of this material at nonzero temperatures and way from the critical field. The resistivity shows a non-Fermi liquid response, the effective mass
of the electron grows and the magnetothermal expansion
of the material is modified all in response to the quantum critical fluctuations.
. This effective temperature would introduce a well defined energy scale in the problem and break the scale invariance of the quantum critical point. On the contrary, it was recently found that certain types of noise can induce a non-equilibrium quantum critical state. This state is out-of-equilibrium because of the continuous energy flow introduced by the noise, but it still retains the scale invariant behavior typical of critical points.
Phase transition
A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....
that takes place at the absolute zero
Absolute zero
Absolute zero is the theoretical temperature at which entropy reaches its minimum value. The laws of thermodynamics state that absolute zero cannot be reached using only thermodynamic means....
of temperature, typically in a material where the phase transition temperature has been driven to zero by the application of a pressure, field or through doping.
Conventional phase transitions occur at finite temperature, when the growth of random thermal fluctuations
Thermal fluctuations
In statistical mechanics, thermal fluctuations are random deviations of a system from its equilibrium. All thermal fluctuations become larger and more frequent as the temperature increases, and likewise they disappear altogether as temperature approaches absolute zero.Thermal fluctuations are a...
leads to a
change in the physical state of a system. Condensed matter physics
Condensed matter physics
Condensed matter physics deals with the physical properties of condensed phases of matter. These properties appear when a number of atoms at the supramolecular and macromolecular scale interact strongly and adhere to each other or are otherwise highly concentrated in a system. The most familiar...
research over the past few decades has revealed a new class of phase transitions, called a quantum phase transition
Quantum phase transition
In physics, a quantum phase transition is a phase transition between different quantum phases . Contrary to classical phase transitions, quantum phase transitions can only be accessed by varying a physical parameter - such as magnetic field or pressure - at absolute zero temperature...
, which take place at absolute zero
Absolute zero
Absolute zero is the theoretical temperature at which entropy reaches its minimum value. The laws of thermodynamics state that absolute zero cannot be reached using only thermodynamic means....
, and which are
driven by the zero point quantum fluctuations associated with Heisenberg's uncertainty principle
Uncertainty principle
In quantum mechanics, the Heisenberg uncertainty principle states a fundamental limit on the accuracy with which certain pairs of physical properties of a particle, such as position and momentum, can be simultaneously known...
.
Overview
Within the class of phase transitions, there are two main categories: At a first-order phase transition, the properties shift discontinuously, as in the melting of solid, whereas at a second order phase transition, the state of the system changes in a continuous fashion. Second-order phase transitions are marked by the growth of fluctuations on ever-longer length-scales. These fluctuations are called "critical fluctuations". At the critical pointCritical point (thermodynamics)
In physical chemistry, thermodynamics, chemistry and condensed matter physics, a critical point, also called a critical state, specifies the conditions at which a phase boundary ceases to exist...
where a second-order transition occurs the critical fluctuations are scale invariant and extend over the entire system. At a finite temperature phase transition, the fluctuations that develop at a critical point are governed by classical physics, because the characteristic energy of quantum fluctuations is always smaller than the characteristic Boltzmann thermal energy
.At a quantum critical point, the critical fluctuations are quantum mechanical in nature, exhibiting scale invariance in both space and in time. Unlike classical critical points, where the critical fluctuations are limited to a narrow region around the phase transition, the influence of a quantum critical point is felt over a wide range of temperatures above the quantum critical point, so the effect of quantum criticality is felt without ever reaching absolute zero. Quantum criticality was first observed in ferroelectrics
Ferroelectricity
Ferroelectricity is a property of certain materials which possess a spontaneous electric polarization that can be reversed by the application of an external electric field. The term is used in analogy to ferromagnetism, in which a material exhibits a permanent magnetic moment. Ferromagnetism was...
, in which the ferroelectric transition temperature is suppressed to zero.
A wide variety of metallic ferromagnets
Ferromagnetism
Ferromagnetism is the basic mechanism by which certain materials form permanent magnets, or are attracted to magnets. In physics, several different types of magnetism are distinguished...
and antiferromagnets
Antiferromagnetism
In materials that exhibit antiferromagnetism, the magnetic moments of atoms or molecules, usuallyrelated to the spins of electrons, align in a regular pattern with neighboring spins pointing in opposite directions. This is, like ferromagnetism and ferrimagnetism, a manifestation of ordered magnetism...
have been observed to develop quantum critical behavior when their magnetic transition temperature is driven to zero through the application of pressure, chemical doping or magnetic fields. In these cases, the properties of the metal are radically transformed by the critical fluctuations, departing qualitatively from the standard Fermi liquid
Fermi liquid
Fermi liquid theory is a theoretical model of interacting fermions that describes the normal state of most metals at sufficiently low temperatures. The interaction between the particles of the many-body system does not need to be small...
behavior, to form a metallic state sometimes called a non-Fermi liquid or a "strange metal". There is particular interest in these unusual metallic states, which are believed to exhibit a marked preponderence towards the development of superconductivity
Superconductivity
Superconductivity is a phenomenon of exactly zero electrical resistance occurring in certain materials below a characteristic temperature. It was discovered by Heike Kamerlingh Onnes on April 8, 1911 in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum...
.
Quantum critical endpoints
Quantum critical points arise when a susceptibility diverges at zero temperature. There are a number of materials (such as CeNi2Ge2) where this occurs serendipitously. More frequently a material has to be tuned to a quantum critical point. Most commonly this is done by taking a system with a second-order phase transition which occurs at finite temperature and tuning it—for example by applying pressure or magnetic field or changing its chemical composition. CePd2Si2 is such an example, where the antiferromagnetic transition which occurs at about 10K under ambient pressure can be tuned to zero temperature by applying a pressure of 28,000 atmospheres. Less commonly a first-order transition can be made quantum critical. First-order transitions do not normally show critical fluctuations as the material moves discontinuously from one phase into another. However if the first order phase transition does not involve a change of symmetry then the phase diagram can contain a critical endpoint where the first-order phase transition terminates. Such an endpoint has a divergent susceptibility. The transition between the liquid and gas phases is an example of a first-order transition without a change of symmetry and the critical endpoint is characterized by critical fluctuations known as critical opalescenceCritical opalescence
Critical opalescence is a phenomenon which arises in the region of a continuous, or second-order, phase transition. Originally reported by Thomas Andrews in 1869 for the liquid-gas transition in carbon dioxide, many other examples have been discovered since. The phenomenon is most commonly...
.
A quantum critical endpoint arises when a finite temperature critical point is tuned to zero temperature. One of the best studied examples occurs in the layered ruthenate metal, Sr3Ru2O7 in a magnetic field. This material shows metamagnetism
Metamagnetism
Metamagnetism is a blanket term used loosely in physics to describe a sudden increase in the magnetization of a material with a small change in an externally applied magnetic field. The metamagnetic behavior may have quite different physical causes for different types of metamagnets...
with a low-temperature first-order metamagnetic transition where the magnetization jumps when a magnetic field is applied within the directions of the layers. The first-order jump terminates in a critical endpoint at about 1 kelvin. By switching the direction of the magnetic field so that it points almost perpendicular to the layers, the critical endpoint is tuned to zero temperature at a field of about 8 teslas. The resulting quantum critical fluctuations dominate the physical properties of this material at nonzero temperatures and way from the critical field. The resistivity shows a non-Fermi liquid response, the effective mass
Effective mass
In solid state physics, a particle's effective mass is the mass it seems to carry in the semiclassical model of transport in a crystal. It can be shown that electrons and holes in a crystal respond to electric and magnetic fields almost as if they were particles with a mass dependence in their...
of the electron grows and the magnetothermal expansion
Magnetostriction
Magnetostriction is a property of ferromagnetic materials that causes them to change their shape or dimensions during the process of magnetization. The variation of material's magnetization due to the applied magnetic field changes the magnetostrictive strain until reaching its saturation value, λ...
of the material is modified all in response to the quantum critical fluctuations.
Non-equilibrium quantum phase transition
What happens when a quantum critical point is affected by noise? An intuitive guess would be that the external noise defines an effective temperatureEffective temperature
The effective temperature of a body such as a star or planet is the temperature of a black body that would emit the same total amount of electromagnetic radiation...
. This effective temperature would introduce a well defined energy scale in the problem and break the scale invariance of the quantum critical point. On the contrary, it was recently found that certain types of noise can induce a non-equilibrium quantum critical state. This state is out-of-equilibrium because of the continuous energy flow introduced by the noise, but it still retains the scale invariant behavior typical of critical points.